id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1,864 | GUY-A10 | Gilbreath's Conjecture | Define $d_n^k$ by $d_n^1 = p_{n+1} - p_n$ and $d_n^{k+1} = |d_{n+1}^k - d_n^k|$, the successive absolute differences of the sequence of primes. Is it true that $d_1^k = 1$ for all $k$? | Gilbreath conjectured this (and Proth claimed to have proved it long before). This was verified for $k < 63419$ by Killgrove & Ralston. Odlyzko checked it for primes up to $\pi(10^{13})$. Croft and others suggest it has nothing to do with primes as such, but will be true for any sequence consisting of 2 and odd numbers... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | false | {
"id": 1,
"name": "number_theory",
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"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | Duplicate of canonical problem NT-009 ('Gilbreath's Conjecture') | [
"NT-009"
] | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,865 | GUY-A11 | Erdős $100 Problem on Increasing and Decreasing Gaps | Does there exist an $n_0$ such that for every $i$ and $n > n_0$ we have $d_{n+2i} > d_{n+2i+1}$ and $d_{n+2i+1} < d_{n+2i+2}$, where $d_n = p_{n+1} - p_n$? | Erdős & Turán showed that the values of $n$ for which $d_n > d_{n+1}$ have positive lower density, but it is not known if there are infinitely many increasing or decreasing sets of three consecutive values of $d_n$. Erdős offers $100.00 for a proof that such an $n_0$ does not exist. From Richard Guy's "Unsolved Problem... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "unrefereed_claim"
} | Duplicate of canonical problem EP-6 | [
"EP-6"
] | null | null | null | Reconciled with the existing literature review of 2026-08-17: The proposed eventual strict alternation of consecutive prime gaps is false: arbitrarily long strictly increasing and arbitrarily long strictly decreasing runs of consecutive prime gaps exist. This is a consistency correction based on that cited review; the ... | [
{
"url": "https://doi.org/10.4064/aa167-3-4",
"label": "William D. Banks, Tristan Freiberg, and Caroline L. Turnage-Butterbaugh, Consecutive primes in tuples, Acta Arithmetica 167 (2015), 261-266."
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "Unsolve... | 2026-09-27T00:00:00 | William D. Banks, Tristan Freiberg, and Caroline L. Turnage-Butterbaugh, Consecutive primes in tuples, Acta Arithmetica 167 (2015), 261-266.: https://doi.org/10.4064/aa167-3-4 | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,866 | GUY-A13 | Erdős Conjecture on Carmichael Numbers | Let $C(x)$ be the number of Carmichael numbers less than $x$. Does $(\ln C(x))/\ln x$ tend to 1 as $x$ tends to infinity? | Erdős conjectured this behavior for the count of Carmichael numbers. Alford, Granville & Pomerance showed there are infinitely many Carmichael numbers, in fact more than $x^\beta$ of them less than $x$ for $\beta > 0.290306$. Pomerance, Selfridge & Wagstaff give a heuristic argument supporting Erdős' conjecture. From R... | 4 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 4,
"level": 4,
"name": "L4: Expert",
"description": "Very challenging problems at the frontier of mathematical research.",
"color_class": "text-red-600 bg-red-50 border-red-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | Duplicate of canonical problem EP-1057 | [
"EP-1057"
] | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,867 | GUY-A14a | Pomerance's Questions on Good Primes | Call prime $p_n$ good if $p_n^2 > p_{n-i}p_{n+i}$ for all $i$, $1 \le i \le n-1$. Is it true that the set of $n$ for which $p_n$ is good has density 0? Are there infinitely many $n$ with $p_n p_{n+1} > p_{n-i} p_{n+1+i}$ for all $i$, $1 \le i \le n-1$? | Erdős and Straus introduced the concept of good primes. Examples include 5, 11, 17, and 29. Pomerance used the prime number graph to show there are infinitely many good primes and posed several related questions. From Richard Guy's "Unsolved Problems in Number Theory", Section A14.
<!-- LITERATURE-TRIAGE:BEGIN -->
## ... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | false | {
"id": 1,
"name": "number_theory",
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 9,
"name": "guy_prime_numbers",
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"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | Duplicate of canonical problem EP-453 | [
"EP-453"
] | null | [Discussion #4 literature review, 2026-10-08] `10.1090/S0025-5718-1979-0514821-1` → `10.1090/S0025-5718-1979-0514836-7`. | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,868 | GUY-A15 | Congruent Products of Consecutive Numbers | What is the least prime $p$ such that there are integers $a, k_1, k_2, k_3$ with $\prod_{i=1}^{k_1} (a+i) \equiv \prod_{i=1}^{k_2} (a+k_1+i) \equiv \prod_{i=1}^{k_3} (a+k_1+k_2+i) \equiv 1 \pmod{p}$? | Erdős observed that $3 \cdot 4 \equiv 5 \cdot 6 \cdot 7 \equiv 1 \pmod{11}$ and suggested that such primes $p$ exist for any number of congruent products. Narkiewicz and others found examples for larger numbers of terms. From Richard Guy's "Unsolved Problems in Number Theory", Section A15.
<!-- LITERATURE-TRIAGE:BEGIN... | 2 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
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"slug": "number-theory",
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"created_at": "2026-07-31T15:26:25.670Z"
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"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | {
"source_url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "unrefereed_claim"
} | Duplicate of canonical problem EP-677 | [
"EP-677"
] | null | null | null | Reconciled with the existing literature review of 2026-08-17: The least prime is 17. This is a consistency correction based on that cited review; the discussion does not independently re-verify its proof claims.
**What remains.** Nothing remains for the stated least-prime question; analogous least primes for larger nu... | [
{
"url": "https://oeis.org/A060427",
"label": "OEIS Foundation, A060427, Smallest prime p such that there are n strings of consecutive integers all having products = 1 mod p, updated 2026-07-27."
},
{
"url": "https://huggingface.co/datasets/ulamai/UnsolvedMath/discussions/4",
"label": "UnsolvedM... | 2026-09-27T00:00:00 | OEIS Foundation, A060427, Smallest prime p such that there are n strings of consecutive integers all having products = 1 mod p, updated 2026-07-27.: https://oeis.org/A060427 | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,869 | GUY-A16 | Walking to Infinity on Gaussian Primes | Can one walk from the origin to infinity using Gaussian primes as stepping stones and taking steps of bounded length? | Motzkin and Gordon asked this question about Gaussian primes (primes in the ring of complex numbers $a+bi$ where $a, b$ are integers). Presumably not. Jordan & Rabung showed that steps of length at least 4 are necessary. Gethner, Wagon & Wick produced a moat of width $\sqrt{26}$. From Richard Guy's "Unsolved Problems i... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | Duplicate of canonical problem EP-952 | [
"EP-952"
] | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,870 | GUY-A17 | Giuga's Conjecture on Prime Characterization | Is it true that if $n$ divides $1^{n-1} + 2^{n-1} + \dots + (n-1)^{n-1} + 1$, then $n$ is prime? | Sierpiński observed that if $n$ is prime, then $n$ divides this sum. Giuga conjectured the converse and verified it for $n \le 10^{1000}$. A counterexample would be a Carmichael number with additional properties. An equivalent conjecture is $n B_{n-1} \equiv -1 \pmod{n}$ where $B_k$ are Bernoulli numbers. From Richard ... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,871 | GUY-A18 | Erdős-Selfridge Classification: Infinitely Many Primes in Each Class | In the Erdős-Selfridge classification of primes, are there infinitely many primes in each class? Prime $p$ is in class 1 if the only prime divisors of $p+1$ are 2 or 3; and $p$ is in class $r$ if every prime factor of $p+1$ is in some class $\le r-1$, with equality for at least one prime factor. | The first few classes are: Class 1: 2, 3, 5, 7, 11, 17, 23, 31, 47, 53, 71, 107, 127, 191, ...; Class 2: 13, 19, 29, 41, 43, 59, 61, 67, 79, 83, 89, 97, 101, ...; Class 3: 37, 103, 113, 151, 157, 163, 173, 181, 193, 227, 233, ... From Richard Guy's "Unsolved Problems in Number Theory", Section A18.
<!-- LITERATURE-TRI... | 3 | open | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,872 | GUY-A19a | Erdős Conjecture on $n - 2^k$ Prime | Are 4, 7, 15, 21, 45, 75, and 105 the only values of $n$ for which $n - 2^k$ is prime for all $k$ such that $2 \le 2^k < n$? | Erdős conjectures that these are the only such values. He also conjectures that for infinitely many $n$, all the integers $n - 2^k, 1 \le 2^k < n$ are squarefree. From Richard Guy's "Unsolved Problems in Number Theory", Section A19.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-17)
**Status:*... | 3 | open | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
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"slug": "number-theory",
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"created_at": "2026-07-31T15:26:25.670Z"
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"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | Duplicate of canonical problem EP-1142 | [
"EP-1142"
] | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,873 | GUY-A19b | Cohen-Selfridge Problem on $\pm p^a \pm 2^b$ | What is the least positive odd number not of the form $\pm p^a \pm 2^b$, where $p$ is an odd prime? | Cohen & Selfridge observed that the number is greater than $2^{18}$. This is related to the representation of odd numbers as sums or differences of prime powers and powers of 2. From Richard Guy's "Unsolved Problems in Number Theory", Section A19.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature review (checked 2026-08-... | 2 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 2,
"level": 2,
"name": "L2: Intermediate",
"description": "Challenging problems requiring solid mathematical background. Reserved for future additions.",
"color_class": "text-blue-600 bg-blue-50 border-blue-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | null | null | null | [Discussion #4 literature review, 2026-10-08] `10.1016/j.jnt.2007.06.003` is a paper by Kurokawa; cited paper: `10.1090/S0002-9939-99-05502-1` (Sun, Proc. Amer. Math. Soc. 128 (2000), 997–1002, not J. Number Theory). | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,874 | GUY-A20 | Density of Symmetric Primes | Given pairs of odd primes $p, q$, define $S(q,p)$ as the number of lattice points $(m, n)$ in the rectangle $0 < m < p/2$, $0 < n < q/2$ below the diagonal. A pair is symmetric if $S(p, q) = S(q,p)$. Is the number of symmetric primes less than $x$ equal to $x/(\ln x)^{\sigma+o(1)}$, where $\sigma = 2 - (1+\ln \ln 2)/\l... | Fletcher, Lindgren & Pomerance showed that a pair is symmetric just if $|p - q| = (p - 1, q - 1)$, and that the number of symmetric primes less than $x$ is at most $x/(\ln x)^{1.027}$. They conjectured the more precise asymptotic. From Richard Guy's "Unsolved Problems in Number Theory", Section A20.
<!-- LITERATURE-TR... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
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"level": 3,
"name": "L3: Advanced",
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"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
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"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,875 | GUY-A12a | Square Pseudoprimes | Are there any square pseudoprimes (base 2) other than multiples of $1194649 = 1093^2$ or $12327121 = 3511^2$? | Pinch observed that there are 54 non-squarefree pseudoprimes up to $10^{13}$, all multiples of $1093^2$ or $3511^2$. The question asks if there are other perfect squares that are pseudoprimes to base 2. From Richard Guy's "Unsolved Problems in Number Theory", Section A12.
<!-- LITERATURE-TRIAGE:BEGIN -->
## Literature... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
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"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,876 | GUY-A12b | Selfridge-Wagstaff-Pomerance Prize Problem | Does there exist a composite number $n \equiv 3$ or $7 \pmod{10}$ which divides both $2^n - 2$ and the Fibonacci number $u_{n+1}$? | Selfridge, Wagstaff & Pomerance offer $500 + $100 + $20 = $620 for finding such a composite $n$, or $20 + $100 + $500 = $620 for a proof that no such $n$ exists. This combines pseudoprime properties with Fibonacci divisibility. From Richard Guy's "Unsolved Problems in Number Theory", Section A12.
<!-- LITERATURE-TRIAG... | 3 | partially_solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
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"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,877 | GUY-A12c | Even Fibonacci Pseudoprimes | Does there exist an even Fibonacci pseudoprime? | A Fibonacci pseudoprime of the $m$-th kind is an odd composite integer $n$ with $V_n(m, -1) \equiv m \pmod n$ where $V_n$ is the Lucas sequence. Somer showed that if an even Fibonacci pseudoprime exists, it must be greater than $28 \times 10^{12}$. From Richard Guy's "Unsolved Problems in Number Theory", Section A12.
... | 3 | solved | null | null | 1 | 9 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 9,
"name": "guy_prime_numbers",
"display_name": "Richard Guy - A: Prime Numbers",
"description": "Problems from Chapter A (Prime Numbers) of Richard Guy's \"Unsolved Problems in Number Theory\", a comprehensive collection of open questions in prime number theory.",
"slug": "guy-prime-numbers",
"orde... | null | {
"source_url": "https://doi.org/10.1007/978-94-011-3586-3_31",
"checked_at": "2026-10-08",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-08] **solved (no, for the first kind; the statement needs that qualifier)**. The record asks whether an even Fibonacci pseudoprime exists and cites L. Somer's bound; in Somer's paper ([Applications of Fibonacci Numbers 4 (1991), 277–288](https://doi.org/10.1007/978-94-011-3586-... | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
1,878 | EP-1 | Erdős Problem #1 | If $A\subseteq \{1,\ldots,N\}$ with $\lvert A\rvert=n$ is such that the subset sums $\sum_{a\in S}a$ are distinct for all $S\subseteq A$ then\[N \gg 2^{n}.\] | Erdős Problems (#1, https://www.erdosproblems.com/1). Maintainer status: DISPROVED (LEAN). Erdős prize: $500. OEIS: A276661. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.1). | 3 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/1",
"checked_at": "2026-10-08",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-08] **solved (no)**. This is the statement of Erdős problem 1, which the dataset already labels solved (`EP-1`; [erdosproblems.com/1](https://www.erdosproblems.com/1): disproved, with a proof verified in Lean). We read the statements, not the proof. | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | The maintained Erdős Problems source lists problem 1 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/1",
"label": "Erdős Problems #1: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://hugging... | 2026-09-27T00:00:00 | Erdős Problems #1: disproved (Lean): https://www.erdosproblems.com/1
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/1 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,879 | EP-3 | Erdős Problem #3 | If $A\subseteq \mathbb{N}$ has $\sum_{n\in A}\frac{1}{n}=\infty$ then must $A$ contain arbitrarily long arithmetic progressions? | Erdős Problems (#3, https://www.erdosproblems.com/3). Maintainer status: OPEN. Erdős prize: $5000. OEIS: A003002, A003003, A003004, A003005. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.3). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"GUY-A5b"
] | {
"source_url": "https://www.erdosproblems.com/3",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/3 | Erdős Problems (erdosproblems.com) | $5000 | [] | null | null | null | null | null | null | null | null | null | null |
1,880 | EP-5 | Erdős Problem #5 | Let $C\geq 0$. Is there an infinite sequence of $n_i$ such that\[\lim_{i\to \infty}\frac{p_{n_i+1}-p_{n_i}}{\log n_i}=C?\] | Erdős Problems (#5, https://www.erdosproblems.com/5). Maintainer status: OPEN. OEIS: A001223. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.5). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/5",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | [Discussion #4 literature review, 2026-10-08] `10.1112/plms/pdw037` is a paper by Fujita; cited paper: `10.1112/plms/pdw036`. | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/5 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,881 | EP-9 | Erdős Problem #9 | Let $A$ be the set of all odd integers $\geq 1$ not of the form $p+2^{k}+2^l$ (where $k,l\geq 0$ and $p$ is prime). Is the upper density of $A$ positive? | Erdős Problems (#9, https://www.erdosproblems.com/9). Maintainer status: OPEN. OEIS: A006286. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.9). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/9",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/9 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,882 | EP-10 | Erdős Problem #10 | Is there some $k$ such that every large integer is the sum of a prime and at most $k$ powers of 2? | Erdős Problems (#10, https://www.erdosproblems.com/10). Maintainer status: OPEN. OEIS: A387053. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.10). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/10",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/10 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,883 | EP-12 | Erdős Problem #12 | Let $A$ be an infinite set such that there are no distinct $a,b,c\in A$ such that $a\mid (b+c)$ and $b,c>a$. Is there such an $A$ with\[\liminf \frac{\lvert A\cap\{1,\ldots,N\}\rvert}{N^{1/2}}>0?\]Does there exist some absolute constant $c>0$ such that there are always infinitely many $N$ with\[\lvert A\cap\{1,\ldots,N... | Erdős Problems (#12, https://www.erdosproblems.com/12). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.12). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/12",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/12 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,884 | EP-14 | Erdős Problem #14 | Let $A\subseteq \mathbb{N}$. Let $B\subseteq \mathbb{N}$ be the set of integers which are representable in exactly one way as the sum of two elements from $A$.
Is it true that for all $\epsilon>0$ and large $N$\[\lvert \{1,\ldots,N\}\backslash B\rvert \gg_\epsilon N^{1/2-\epsilon}?\]Is it possible that\[\lvert \{1,\ld... | Erdős Problems (#14, https://www.erdosproblems.com/14). Maintainer status: OPEN. OEIS: A143824. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.14). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/14",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/14 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,885 | EP-15 | Erdős Problem #15 | Is it true that\[\sum_{n=1}^\infty(-1)^n\frac{n}{p_n}\]converges, where $p_n$ is the sequence of primes? | Erdős Problems (#15, https://www.erdosproblems.com/15). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.15). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/15",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/15 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,886 | EP-17 | Erdős Problem #17 | Are there infinitely many primes $p$ such that every even number $n\leq p-3$ can be written as a difference of primes $n=q_1-q_2$ where $q_1,q_2\leq p$? | Erdős Problems (#17, https://www.erdosproblems.com/17). Maintainer status: OPEN. cluster primes OEIS: A038133. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.17). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/17",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | cluster primes | [
"erdos-problems",
"number-theory",
"primes"
] | null | null | null | null | https://www.erdosproblems.com/17 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,887 | EP-18 | Erdős Problem #18 | We call $m$ practical if every integer $1\leq n<m$ is the sum of distinct divisors of $m$. If $m$ is practical then let $h(m)$ be such that $h(m)$ many divisors always suffice.
Are there infinitely many practical $m$ such that\[h(m) < (\log\log m)^{O(1)}?\]Is it true that $h(n!)<n^{o(1)}$? Or perhaps even $h(n!)<(\log... | Erdős Problems (#18, https://www.erdosproblems.com/18). Maintainer status: OPEN. practical numbers OEIS: A005153. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.18). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/18",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | practical numbers | [
"erdos-problems",
"number-theory",
"divisors",
"factorials"
] | null | null | null | null | https://www.erdosproblems.com/18 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,888 | EP-20 | Erdős Problem #20 | Let $f(n,k)$ be minimal such that every family $\mathcal{F}$ of $n$-uniform sets with $\lvert \mathcal{F}\rvert \geq f(n,k)$ contains a $k$-sunflower. Is it true that\[f(n,k) < c_k^n\]for some constant $c_k>0$? | Erdős Problems (#20, https://www.erdosproblems.com/20). Maintainer status: OPEN. Erdős prize: $1000. sunflower conjecture OEIS: A332077. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.20). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"COMB-015",
"COMB-006",
"COMB-020"
] | {
"source_url": "https://www.erdosproblems.com/20",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | sunflower conjecture
[Discussion #4 literature review, 2026-10-08] `10.1016/j.disc.2020.112157` is a paper by Albrecht; cited paper: `10.1016/j.disc.2021.112367`. | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/20 | Erdős Problems (erdosproblems.com) | $1000 | [] | null | null | null | null | null | null | null | null | null | null |
1,889 | EP-25 | Erdős Problem #25 | Let $1\leq n_1<n_2<\cdots$ be an arbitrary sequence of integers, each with an associated residue class $a_i\pmod{n_i}$. Let $A$ be the set of integers $n$ such that for every $i$ either $n<n_i$ or $n\not\equiv a_i\pmod{n_i}$. Must the logarithmic density of $A$ exist? | Erdős Problems (#25, https://www.erdosproblems.com/25). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.25). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/25",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/25 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,890 | EP-28 | Erdős Problem #28 | If $A\subseteq \mathbb{N}$ is such that $A+A$ contains all but finitely many integers then $\limsup 1_A\ast 1_A(n)=\infty$. | Erdős Problems (#28, https://www.erdosproblems.com/28). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.28). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/28",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/28 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,891 | EP-30 | Erdős Problem #30 | Let $h(N)$ be the maximum size of a Sidon set in $\{1,\ldots,N\}$. Is it true that, for every $\epsilon>0$,\[h(N) = N^{1/2}+O_\epsilon(N^\epsilon)?\] | Erdős Problems (#30, https://www.erdosproblems.com/30). Maintainer status: OPEN. Erdős prize: $1000. OEIS: A143824, A227590, A003022. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.30). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/30",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/30 | Erdős Problems (erdosproblems.com) | $1000 | [] | null | null | null | null | null | null | null | null | null | null |
1,892 | EP-32 | Erdős Problem #32 | Is there a set $A\subset\mathbb{N}$ such that\[\lvert A\cap\{1,\ldots,N\}\rvert = o((\log N)^2)\]and such that every large integer can be written as $p+a$ for some prime $p$ and $a\in A$?
Can the bound $O(\log N)$ be achieved? Must such an $A$ satisfy\[\liminf \frac{\lvert A\cap\{1,\ldots,N\}\rvert}{\log N}> 1?\] | Erdős Problems (#32, https://www.erdosproblems.com/32). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.32). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/32",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/32 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,893 | EP-33 | Erdős Problem #33 | Let $A\subset\mathbb{N}$ be such that every large integer can be written as $n^2+a$ for some $a\in A$ and $n\geq 0$. What is the smallest possible value of\[\limsup \frac{\lvert A\cap\{1,\ldots,N\}\rvert}{N^{1/2}}?\]Is\[\liminf \frac{\lvert A\cap\{1,\ldots,N\}\rvert}{N^{1/2}}>1?\] | Erdős Problems (#33, https://www.erdosproblems.com/33). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.33). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/33",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/33 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,894 | EP-36 | Erdős Problem #36 | Find the optimal constant $c>0$ such that the following holds.
For all sufficiently large $N$, if $A\sqcup B=\{1,\ldots,2N\}$ is a partition into two equal parts, so that $\lvert A\rvert=\lvert B\rvert=N$, then there is some $x$ such that the number of solutions to $a-b=x$ with $a\in A$ and $b\in B$ is at least $cN$. | Erdős Problems (#36, https://www.erdosproblems.com/36). Maintainer status: OPEN. minimum overlap problem OEIS: A393584. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.36). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/36",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | minimum overlap problem | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/36 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,895 | EP-38 | Erdős Problem #38 | Does there exist $B\subset\mathbb{N}$ which is not an additive basis, but is such that for every set $A\subseteq\mathbb{N}$ of Schnirelmann density $\alpha$ and every $N$ there exists $b\in B$ such that\[\lvert (A\cup (A+b))\cap \{1,\ldots,N\}\rvert\geq (\alpha+f(\alpha))N\]where $f(\alpha)>0$ for $0<\alpha <1 $?
The ... | Erdős Problems (#38, https://www.erdosproblems.com/38). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.38). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/38",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | The maintained Erdős Problems source lists problem 38 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/38",
"label": "Erdős Problems #38: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggingf... | 2026-09-27T00:00:00 | Erdős Problems #38: proved (Lean): https://www.erdosproblems.com/38
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/38 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,896 | EP-39 | Erdős Problem #39 | Is there an infinite Sidon set $A\subset \mathbb{N}$ such that\[\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}\]for all $\epsilon>0$? | Erdős Problems (#39, https://www.erdosproblems.com/39). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.39). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/39",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/39 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,897 | EP-40 | Erdős Problem #40 | For what functions $g(N)\to \infty$ is it true that\[\lvert A\cap \{1,\ldots,N\}\rvert \gg \frac{N^{1/2}}{g(N)}\]implies $\limsup 1_A\ast 1_A(n)=\infty$? | Erdős Problems (#40, https://www.erdosproblems.com/40). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.40). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/40",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/40 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,898 | EP-41 | Erdős Problem #41 | Let $A\subset\mathbb{N}$ be an infinite set such that the triple sums $a+b+c$ are all distinct for $a,b,c\in A$ (aside from the trivial coincidences). Is it true that\[\liminf \frac{\lvert A\cap \{1,\ldots,N\}\rvert}{N^{1/3}}=0?\] | Erdős Problems (#41, https://www.erdosproblems.com/41). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.41). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/41",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | [Discussion #4 literature review, 2026-10-08] [arXiv:1206.3087](https://arxiv.org/abs/1206.3087): Rafael Tesoro (cited: Carlos Tesoro). | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/41 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,899 | EP-42 | Erdős Problem #42 | Let $M\geq 1$ and $N$ be sufficiently large in terms of $M$. Is it true that for every Sidon set $A\subset \{1,\ldots,N\}$ there is another Sidon set $B\subset \{1,\ldots,N\}$ of size $M$ such that $(A-A)\cap(B-B)=\{0\}$? | Erdős Problems (#42, https://www.erdosproblems.com/42). Maintainer status: SOLVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.42). | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/42",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | The maintained Erdős Problems source lists problem 42 as “solved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/42",
"label": "Erdős Problems #42: solved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggingf... | 2026-09-27T00:00:00 | Erdős Problems #42: solved (Lean): https://www.erdosproblems.com/42
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/42 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,900 | EP-43 | Erdős Problem #43 | If $A,B\subset \{1,\ldots,N\}$ are two Sidon sets such that $(A-A)\cap(B-B)=\{0\}$ then is it true that\[ \binom{\lvert A\rvert}{2}+\binom{\lvert B\rvert}{2}\leq\binom{f(N)}{2}+O(1),\]where $f(N)$ is the maximum possible size of a Sidon set in $\{1,\ldots,N\}$? If $\lvert A\rvert=\lvert B\rvert$ then can this bound be ... | Erdős Problems (#43, https://www.erdosproblems.com/43). Maintainer status: DISPROVED (LEAN). Erdős prize: $100. OEIS: A143824, A227590, A003022. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.43). | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/43",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | The maintained Erdős Problems source lists problem 43 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/43",
"label": "Erdős Problems #43: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggi... | 2026-09-27T00:00:00 | Erdős Problems #43: disproved (Lean): https://www.erdosproblems.com/43
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/43 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,901 | EP-44 | Erdős Problem #44 | Let $N\geq 1$ and $A\subset \{1,\ldots,N\}$ be a Sidon set. Is it true that, for any $\epsilon>0$, there exist $M$ and $B\subset \{N+1,\ldots,M\}$ (which may depend on $N,A,\epsilon$) such that $A\cup B\subset \{1,\ldots,M\}$ is a Sidon set of size at least $(1-\epsilon)M^{1/2}$? | Erdős Problems (#44, https://www.erdosproblems.com/44). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.44). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/44",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | [Discussion #4 literature review, 2026-10-08] `10.11606/resimeusp.v2i2.74798` (no DOI found for the cited paper). | [
"erdos-problems",
"number-theory",
"sidon-sets",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/44 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,902 | EP-50 | Erdős Problem #50 | Schoenberg proved that for every $c\in [0,1]$ the density of\[\{ n\in \mathbb{N}: \phi(n)<cn\}\]exists. Let this density be denoted by $f(c)$. Is it true that there are no $x$ such that $f'(x)$ exists and is positive? | Erdős Problems (#50, https://www.erdosproblems.com/50). Maintainer status: OPEN. Erdős prize: $250. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.50). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/50",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/50 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,903 | EP-51 | Erdős Problem #51 | Is there an infinite set $A\subset \mathbb{N}$ such that for every $a\in A$ there is an integer $n$ such that $\phi(n)=a$, and yet if $n_a$ is the smallest such integer then $n_a/a\to \infty$ as $a\to\infty$? | Erdős Problems (#51, https://www.erdosproblems.com/51). Maintainer status: OPEN. OEIS: A002202, A014197. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.51). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/51",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/51 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,904 | EP-52 | Erdős Problem #52 | Let $A$ be a finite set of integers. Is it true that for every $\epsilon>0$\[\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?\] | Erdős Problems (#52, https://www.erdosproblems.com/52). Maintainer status: OPEN. Erdős prize: $250. sum-product problem OEIS: A263996. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.52). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/52",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | sum-product problem | [
"erdos-problems",
"number-theory",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/52 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,905 | EP-60 | Erdős Problem #60 | Does every graph on $n$ vertices with $>\mathrm{ex}(n;C_4)$ edges contain $\gg n^{1/2}$ many copies of $C_4$? | Erdős Problems (#60, https://www.erdosproblems.com/60). Maintainer status: OPEN. OEIS: A006855. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.60). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/60",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/60 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,906 | EP-61 | Erdős Problem #61 | For any graph $H$ is there some $c=c(H)>0$ such that every graph $G$ on $n$ vertices that does not contain $H$ as an induced subgraph contains either a complete graph or independent set on $\geq n^c$ vertices? | Erdős Problems (#61, https://www.erdosproblems.com/61). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.61). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/61",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/61 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,907 | EP-62 | Erdős Problem #62 | If $G_1,G_2$ are two graphs with chromatic number $\aleph_1$ then must there exist a graph $G$ whose chromatic number is $4$ (or even $\aleph_0$) which is a subgraph of both $G_1$ and $G_2$? | Erdős Problems (#62, https://www.erdosproblems.com/62). Maintainer status: OPEN. | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/62",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/62 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,908 | EP-65 | Erdős Problem #65 | Let $G$ be a graph with $n$ vertices and $kn$ edges, and $a_1<a_2<\cdots $ be the lengths of cycles in $G$. Is it true that\[\sum\frac{1}{a_i}\gg \log k?\]Is the sum $\sum\frac{1}{a_i}$ minimised when $G$ is a complete bipartite graph? | Erdős Problems (#65, https://www.erdosproblems.com/65). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.65). | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/65",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/65 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,909 | EP-66 | Erdős Problem #66 | Is there $A\subseteq \mathbb{N}$ such that\[\lim_{n\to \infty}\frac{1_A\ast 1_A(n)}{\log n}\]exists and is $\neq 0$? | Erdős Problems (#66, https://www.erdosproblems.com/66). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.66). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/66",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"additive-basis"
] | null | null | null | null | https://www.erdosproblems.com/66 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,910 | EP-68 | Erdős Problem #68 | Is\[\sum_{n\geq 2}\frac{1}{n!-1}\]irrational? | Erdős Problems (#68, https://www.erdosproblems.com/68). Maintainer status: OPEN. OEIS: A331373. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.68). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/68",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"irrationality"
] | null | null | null | null | https://www.erdosproblems.com/68 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,911 | EP-70 | Erdős Problem #70 | Let $\mathfrak{c}$ be the ordinal of the real numbers, $\beta$ be any countable ordinal, and $2\leq n<\omega$. Is it true that $\mathfrak{c}\to (\beta, n)_2^3$? | Erdős Problems (#70, https://www.erdosproblems.com/70). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.70). | 1 | open | null | null | 10 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 10,
"name": "set_theory",
"display_name": "Set Theory",
"description": "Foundations of mathematics, infinite sets, and cardinality.",
"slug": "set-theory",
"order_index": 10,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/70",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory",
"set-theory"
] | null | null | null | null | https://www.erdosproblems.com/70 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,912 | EP-74 | Erdős Problem #74 | Let $f(n)\to \infty$ (possibly very slowly). Is there a graph of infinite chromatic number such that every finite subgraph on $n$ vertices can be made bipartite by deleting at most $f(n)$ edges? | Erdős Problems (#74, https://www.erdosproblems.com/74). Maintainer status: DISPROVED (LEAN). Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.74). | 1 | solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/74",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number",
"cycles"
] | The maintained Erdős Problems source lists problem 74 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/74",
"label": "Erdős Problems #74: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggi... | 2026-09-27T00:00:00 | Erdős Problems #74: disproved (Lean): https://www.erdosproblems.com/74
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/74 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,913 | EP-75 | Erdős Problem #75 | Is there a graph of chromatic number $\aleph_1$ with $\aleph_1$ vertices such that for all $\epsilon>0$ if $n$ is sufficiently large and $H$ is a subgraph on $n$ vertices then $H$ contains an independent set of size $>n^{1-\epsilon}$?
What about an independent set of size $\gg n$? | Erdős Problems (#75, https://www.erdosproblems.com/75). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.75). | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/75",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/75 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,914 | EP-77 | Erdős Problem #77 | If $R(k)$ is the Ramsey number for $K_k$, the minimal $n$ such that every $2$-colouring of the edges of $K_n$ contains a monochromatic copy of $K_k$, then find the value of\[\lim_{k\to \infty}R(k)^{1/k}.\] | Erdős Problems (#77, https://www.erdosproblems.com/77). Maintainer status: OPEN. Erdős prize: $250. OEIS: A059442. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.77). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/77",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/77 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,915 | EP-78 | Erdős Problem #78 | Let $R(k)$ be the Ramsey number for $K_k$, the minimal $n$ such that every $2$-colouring of the edges of $K_n$ contains a monochromatic copy of $K_k$.
Give a constructive proof that $R(k)>C^k$ for some constant $C>1$. | Erdős Problems (#78, https://www.erdosproblems.com/78). Maintainer status: OPEN. Erdős prize: $100. OEIS: A059442. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.78). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/78",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/78 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,916 | EP-80 | Erdős Problem #80 | Let $c>0$ and let $f_c(n)$ be the maximal $m$ such that every graph $G$ with $n$ vertices and at least $cn^2$ edges, where each edge is contained in at least one triangle, must contain a book of size $m$, that is, an edge shared by at least $m$ different triangles.
Estimate $f_c(n)$. In particular, is it true that $f_... | Erdős Problems (#80, https://www.erdosproblems.com/80). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.80). | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/80",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/80 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,917 | EP-81 | Erdős Problem #81 | Let $G$ be a chordal graph on $n$ vertices - that is, $G$ has no induced cycles of length greater than $3$. Can the edges of $G$ be partitioned into $n^2/6+O(n)$ many cliques? | Erdős Problems (#81, https://www.erdosproblems.com/81). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.81). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/81",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/81 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,918 | EP-82 | Erdős Problem #82 | Let $F(n)$ be maximal such that every graph on $n$ vertices contains a regular induced subgraph on at least $F(n)$ vertices. Prove that $F(n)/\log n\to \infty$. | Erdős Problems (#82, https://www.erdosproblems.com/82). Maintainer status: OPEN. OEIS: A120414, A390256, A390257, A390919, A392636, A394400, A394462, A394539, A394563, A394564, A394573, A394574, A394930, A394933. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.82). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/82",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/82 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,919 | EP-84 | Erdős Problem #84 | The cycle set of a graph $G$ on $n$ vertices is a set $A\subseteq \{3,\ldots,n\}$ such that there is a cycle in $G$ of length $\ell$ if and only if $\ell \in A$. Let $f(n)$ count the number of possible such $A$.
Prove that $f(n)=o(2^n)$.
Prove that $f(n)/2^{n/2}\to \infty$. | Erdős Problems (#84, https://www.erdosproblems.com/84). Maintainer status: OPEN. OEIS: A399654. | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/84",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/84 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,920 | EP-86 | Erdős Problem #86 | Let $Q_n$ be the $n$-dimensional hypercube graph (so that $Q_n$ has $2^n$ vertices and $n2^{n-1}$ edges). Is it true that every subgraph of $Q_n$ with\[\geq \left(\frac{1}{2}+o(1)\right)n2^{n-1}\]many edges contains a $C_4$? | Erdős Problems (#86, https://www.erdosproblems.com/86). Maintainer status: OPEN. Erdős prize: $100. OEIS: A245762. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.86). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/86",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/86 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,921 | EP-87 | Erdős Problem #87 | Let $\epsilon >0$. Is it true that, if $k$ is sufficiently large, then\[R(G)>(1-\epsilon)^kR(k)\]for every graph $G$ with chromatic number $\chi(G)=k$?
Even stronger, is there some $c>0$ such that, for all large $k$, $R(G)>cR(k)$ for every graph $G$ with chromatic number $\chi(G)=k$? | Erdős Problems (#87, https://www.erdosproblems.com/87). Maintainer status: OPEN. OEIS: A059442. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.87). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/87",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/87 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,922 | EP-89 | Erdős Problem #89 | Does every set of $n$ distinct points in $\mathbb{R}^2$ determine $\gg n/\sqrt{\log n}$ many distinct distances? | Erdős Problems (#89, https://www.erdosproblems.com/89). Maintainer status: OPEN. Erdős prize: $500. Erdős distance problem OEIS: A186704, A131628. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.89). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/89",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | Erdős distance problem | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/89 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,923 | EP-90 | Erdős Problem #90 | Does every set of $n$ distinct points in $\mathbb{R}^2$ contain at most $n^{1+O(1/\log\log n)}$ many pairs which are distance 1 apart? | Erdős Problems (#90, https://www.erdosproblems.com/90). Maintainer status: DISPROVED (LEAN). Erdős prize: $500. unit distance problem OEIS: A186705. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.90). | 1 | solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"GEO-026",
"GEOM-024",
"OPG-778"
] | {
"source_url": "https://www.erdosproblems.com/90",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | unit distance problem | [
"erdos-problems",
"geometry",
"distances"
] | The maintained Erdős Problems source lists problem 90 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/90",
"label": "Erdős Problems #90: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggi... | 2026-09-27T00:00:00 | Erdős Problems #90: disproved (Lean): https://www.erdosproblems.com/90
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/90 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,924 | EP-91 | Erdős Problem #91 | Let $n$ be a sufficiently large integer. Suppose $A\subset \mathbb{R}^2$ has $\lvert A\rvert=n$ and minimises the number of distinct distances between points in $A$. Prove that there are at least two (and probably many) such $A$ which are non-similar. | Erdős Problems (#91, https://www.erdosproblems.com/91). Maintainer status: OPEN. OEIS: A186704. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.91). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/91",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/91 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,925 | EP-92 | Erdős Problem #92 | Let $f(n)$ be maximal such that there exists a set $A$ of $n$ points in $\mathbb{R}^2$ in which every $x\in A$ has at least $f(n)$ points in $A$ equidistant from $x$.
Is it true that $f(n)\leq n^{o(1)}$? Or even $f(n) < n^{O(1/\log\log n)}$? | Erdős Problems (#92, https://www.erdosproblems.com/92). Maintainer status: DISPROVED. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.92). | 1 | solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/92",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | The maintained Erdős Problems source lists problem 92 as “disproved” on 2026-09-27. No Lean verification is inferred from the existence of a formalized statement.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/92",
"label": "Erdős Problems #92: disproved"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggingface.... | 2026-09-27T00:00:00 | Erdős Problems #92: disproved: https://www.erdosproblems.com/92
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/92 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,926 | EP-96 | Erdős Problem #96 | If $n$ points in $\mathbb{R}^2$ form a convex polygon then there are $O(n)$ many pairs which are distance $1$ apart. | Erdős Problems (#96, https://www.erdosproblems.com/96). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.96). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/96",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances",
"convex"
] | null | null | null | null | https://www.erdosproblems.com/96 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,927 | EP-98 | Erdős Problem #98 | Let $h(n)$ be such that any $n$ points in $\mathbb{R}^2$, with no three on a line and no four on a circle, determine at least $h(n)$ distinct distances. Does $h(n)/n\to \infty$? | Erdős Problems (#98, https://www.erdosproblems.com/98). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.98). | 1 | open | null | null | 6 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/98",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/98 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,928 | EP-99 | Erdős Problem #99 | Let $A\subseteq\mathbb{R}^2$ be a set of $n$ points with minimum distance equal to 1, chosen to minimise the diameter of $A$. If $n$ is sufficiently large then must there be three points in $A$ which form an equilateral triangle of size 1? | Erdős Problems (#99, https://www.erdosproblems.com/99). Maintainer status: OPEN. Erdős prize: $100. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.99). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/99",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/99 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,929 | EP-100 | Erdős Problem #100 | Let $A$ be a set of $n$ points in $\mathbb{R}^2$ such that all pairwise distances are at least $1$ and if two distinct distances differ then they differ by at least $1$. Is the diameter of $A$ $\gg n$? | Erdős Problems (#100, https://www.erdosproblems.com/100). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.100). | 1 | open | null | null | 6 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/100",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/100 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,930 | EP-101 | Erdős Problem #101 | Given $n$ points in $\mathbb{R}^2$, no five of which are on a line, the number of lines containing four points is $o(n^2)$. | Erdős Problems (#101, https://www.erdosproblems.com/101). Maintainer status: OPEN. Erdős prize: $100. OEIS: A006065. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.101). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/101",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/101 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,931 | EP-102 | Erdős Problem #102 | Let $c>0$ and $h_c(n)$ be such that for any $n$ points in $\mathbb{R}^2$ such that there are $\geq cn^2$ lines each containing more than three points, there must be some line containing $h_c(n)$ many points. Estimate $h_c(n)$. Is it true that, for fixed $c>0$, we have $h_c(n)\to \infty$? | Erdős Problems (#102, https://www.erdosproblems.com/102). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.102). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/102",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/102 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,932 | EP-103 | Erdős Problem #103 | Let $h(n)$ count the number of incongruent sets of $n$ points in $\mathbb{R}^2$ which minimise the diameter subject to the constraint that $d(x,y)\geq 1$ for all points $x\neq y$. Is it true that $h(n)\to \infty$? | Erdős Problems (#103, https://www.erdosproblems.com/103). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.103). | 1 | open | null | null | 6 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 6,
"name": "geometry",
"display_name": "Geometry",
"description": "Euclidean and non-Euclidean geometry, geometric structures.",
"slug": "geometry",
"order_index": 6,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/103",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/103 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,933 | EP-104 | Erdős Problem #104 | Given $n$ points in $\mathbb{R}^2$ the number of distinct unit circles containing at least three points is $o(n^2)$. | Erdős Problems (#104, https://www.erdosproblems.com/104). Maintainer status: OPEN. Erdős prize: $100. OEIS: A003829. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.104). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/104",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"geometry"
] | null | null | null | null | https://www.erdosproblems.com/104 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,934 | EP-108 | Erdős Problem #108 | For every $r\geq 4$ and $k\geq 2$ is there some finite $f(k,r)$ such that every graph of chromatic number $\geq f(k,r)$ contains a subgraph of girth $\geq r$ and chromatic number $\geq k$? | Erdős Problems (#108, https://www.erdosproblems.com/108). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.108). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/108",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number",
"cycles"
] | null | null | null | null | https://www.erdosproblems.com/108 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,935 | EP-111 | Erdős Problem #111 | If $G$ is a graph let $h_G(n)$ be defined such that any subgraph of $G$ on $n$ vertices can be made bipartite after deleting at most $h_G(n)$ edges.
What is the behaviour of $h_G(n)$? Is it true that $h_G(n)/n\to \infty$ for every graph $G$ with chromatic number $\aleph_1$? | Erdős Problems (#111, https://www.erdosproblems.com/111). Maintainer status: OPEN. | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/111",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number",
"set-theory"
] | null | null | null | null | https://www.erdosproblems.com/111 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,936 | EP-112 | Erdős Problem #112 | Let $k=k(n,m)$ be minimal such that any directed graph on $k$ vertices must contain either an independent set of size $n$ or a transitive tournament of size $m$. Determine $k(n,m)$. | Erdős Problems (#112, https://www.erdosproblems.com/112). Maintainer status: OPEN. | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/112",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | null | null | null | null | https://www.erdosproblems.com/112 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,937 | EP-114 | Erdős Problem #114 | If $p(z)\in\mathbb{C}[z]$ is a monic polynomial of degree $n$ then is the length of the curve $\{ z\in \mathbb{C}: \lvert p(z)\rvert=1\}$ maximised when $p(z)=z^n-1$? | Erdős Problems (#114, https://www.erdosproblems.com/114). Maintainer status: FALSIFIABLE. Erdős prize: $250. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.114). | 1 | partially_solved | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/114",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "falsifiable"
} | null | null | null | null | [
"erdos-problems",
"polynomials",
"analysis"
] | null | null | null | null | https://www.erdosproblems.com/114 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,938 | EP-117 | Erdős Problem #117 | Let $h(n)$ be minimal such that any group $G$ with the property that any subset of $>n$ elements contains some $x\neq y$ such that $xy=yx$ can be covered by at most $h(n)$ many Abelian subgroups.
Estimate $h(n)$ as well as possible. | Erdős Problems (#117, https://www.erdosproblems.com/117). Maintainer status: OPEN. | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/117",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"group-theory"
] | null | null | null | null | https://www.erdosproblems.com/117 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,939 | EP-119 | Erdős Problem #119 | Let $z_i$ be an infinite sequence of complex numbers such that $\lvert z_i\rvert=1$ for all $i\geq 1$, and for $n\geq 1$ let\[p_n(z)=\prod_{i\leq n} (z-z_i).\]Let $M_n=\max_{\lvert z\rvert=1}\lvert p_n(z)\rvert$.
Is it true that $\limsup M_n=\infty$?
Is it true that there exists $c>0$ such that for infinitely many $n... | Erdős Problems (#119, https://www.erdosproblems.com/119). Maintainer status: SOLVED (LEAN). Erdős prize: $100. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.119). | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/119",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "solved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"analysis",
"polynomials"
] | The maintained Erdős Problems source lists problem 119 as “solved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/119",
"label": "Erdős Problems #119: solved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #119: solved (Lean): https://www.erdosproblems.com/119
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/119 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,940 | EP-120 | Erdős Problem #120 | Let $A\subseteq\mathbb{R}$ be an infinite set. Must there be a set $E\subset \mathbb{R}$ of positive measure which does not contain any set of the shape $aA+b$ for some $a,b\in\mathbb{R}$ and $a\neq 0$? | Erdős Problems (#120, https://www.erdosproblems.com/120). Maintainer status: OPEN. Erdős prize: $100. Erdős similarity problem Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.120). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/120",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | Erdős similarity problem
[Discussion #4 literature review, 2026-10-08] . [arXiv:2001.02395](https://arxiv.org/abs/2001.02395) was withdrawn by its authors three days after posting because of a gap in Proposition 3.3; the note could say so instead of calling it a conflicting claim. | [
"erdos-problems",
"combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/120 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,941 | EP-122 | Erdős Problem #122 | For which number theoretic functions $f$ is it true that, for any $F(n)$ such that $F(n)/f(n)\to 0$ for almost all $n$, there are infinitely many $x$ such that\[\frac{\#\{ n\in \mathbb{N}: n+f(n)\in (x,x+F(x))\}}{F(x)}\to \infty?\] | Erdős Problems (#122, https://www.erdosproblems.com/122). Maintainer status: OPEN. | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/122",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/122 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,942 | EP-123 | Erdős Problem #123 | Let $a,b,c> 1$ be three integers which are pairwise coprime. Is every large integer the sum of distinct integers of the form $a^kb^lc^m$ ($k,l,m\geq 0$), none of which divide any other? | Erdős Problems (#123, https://www.erdosproblems.com/123). Maintainer status: PROVED (LEAN). Erdős prize: $250. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.123). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/123",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | The maintained Erdős Problems source lists problem 123 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/123",
"label": "Erdős Problems #123: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #123: proved (Lean): https://www.erdosproblems.com/123
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/123 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,943 | EP-124 | Erdős Problem #124 | For any $d\geq 1$ and $k\geq 0$ let $P(d,k)$ be the set of integers which are the sum of distinct powers $d^i$ with $i\geq k$. Let $3\leq d_1<d_2<\cdots <d_r$ be integers such that\[\sum_{1\leq i\leq r}\frac{1}{d_r-1}\geq 1.\]Can all sufficiently large integers be written as a sum of the shape $\sum_i c_ia_i$ where $c_... | Erdős Problems (#124, https://www.erdosproblems.com/124). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.124). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/124",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"base-representations",
"complete-sequences"
] | null | null | null | null | https://www.erdosproblems.com/124 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,944 | EP-125 | Erdős Problem #125 | Let $A = \{ \sum\epsilon_k3^k: \epsilon_k\in \{0,1\}\}$ be the set of integers which have only the digits $0,1$ when written base $3$, and $B=\{ \sum\epsilon_k4^k: \epsilon_k\in \{0,1\}\}$ be the set of integers which have only the digits $0,1$ when written base $4$.
Does $A+B$ have positive lower density? | Erdős Problems (#125, https://www.erdosproblems.com/125). Maintainer status: DISPROVED (LEAN). OEIS: A367090. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.125). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/125",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"base-representations"
] | The maintained Erdős Problems source lists problem 125 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/125",
"label": "Erdős Problems #125: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://hug... | 2026-09-27T00:00:00 | Erdős Problems #125: disproved (Lean): https://www.erdosproblems.com/125
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/125 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,945 | EP-126 | Erdős Problem #126 | Let $f(n)$ be maximal such that if $A\subseteq\mathbb{N}$ has $\lvert A\rvert=n$ then $\prod_{a\neq b\in A}(a+b)$ has at least $f(n)$ distinct prime factors. Is it true that $f(n)/\log n\to\infty$? | Erdős Problems (#126, https://www.erdosproblems.com/126). Maintainer status: PROVED (LEAN). Erdős prize: $250. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.126). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/126",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | The maintained Erdős Problems source lists problem 126 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/126",
"label": "Erdős Problems #126: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #126: proved (Lean): https://www.erdosproblems.com/126
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/126 | Erdős Problems (erdosproblems.com) | $250 | [] | null | null | null | null | null | null | null | null | null | null |
1,946 | EP-129 | Erdős Problem #129 | Let $R(n;k,r)$ be the smallest $N$ such that if the edges of $K_N$ are $r$-coloured then there is a set of $n$ vertices which does not contain a copy of $K_k$ in at least one of the $r$ colours. Prove that there is a constant $C=C(r)>1$ such that\[R(n;3,r) < C^{\sqrt{n}}.\] | Erdős Problems (#129, https://www.erdosproblems.com/129). Maintainer status: OPEN. ambiguous statement | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/129",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | ambiguous statement | [
"erdos-problems",
"graph-theory",
"ramsey-theory"
] | The maintained Erdős Problems source still lists #129 as “open” on 2026-09-27. The August literature triage claimed a resolution, but the discussion explicitly flags that conclusion as unverified. That claim is not accepted as a full solution here.
**What remains.** Resolve the discrepancy between the earlier triage c... | [
{
"url": "https://www.erdosproblems.com/129",
"label": "Erdős Problems #129: open"
},
{
"url": "https://www.erdosproblems.com/129",
"label": "Thomas F. Bloom, Erdős Problem #129, with disproof attributed to Antonio Girão, accessed 2026-08-17."
},
{
"url": "https://www.erdosproblems.com/l... | 2026-09-27T00:00:00 | null | https://www.erdosproblems.com/129 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,947 | EP-130 | Erdős Problem #130 | Let $A\subset\mathbb{R}^2$ be an infinite set which contains no three points on a line and no four points on a circle. Consider the graph with vertices the points in $A$, where two vertices are joined by an edge if and only if they are an integer distance apart.
How large can the chromatic number and clique number of ... | Erdős Problems (#130, https://www.erdosproblems.com/130). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.130). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/130",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"chromatic-number"
] | null | null | null | null | https://www.erdosproblems.com/130 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,948 | EP-131 | Erdős Problem #131 | Let $F(N)$ be the maximal size of $A\subseteq\{1,\ldots,N\}$ such that no $a\in A$ divides the sum of any distinct elements of $A\backslash\{a\}$. Estimate $F(N)$. In particular, is it true that\[F(N) > N^{1/2-o(1)}?\] | Erdős Problems (#131, https://www.erdosproblems.com/131). Maintainer status: OPEN. OEIS: A068063. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.131). | 1 | partially_solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/131",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/131 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,949 | EP-132 | Erdős Problem #132 | Let $A\subset \mathbb{R}^2$ be a set of $n$ points. Must there be two distances which occur at least once but between at most $n$ pairs of points? Must the number of such distances $\to \infty$ as $n\to \infty$? | Erdős Problems (#132, https://www.erdosproblems.com/132). Maintainer status: OPEN. Erdős prize: $100. | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/132",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"distances"
] | null | null | null | null | https://www.erdosproblems.com/132 | Erdős Problems (erdosproblems.com) | $100 | [] | null | null | null | null | null | null | null | null | null | null |
1,950 | EP-137 | Erdős Problem #137 | We say that $N$ is powerful if whenever $p\mid N$ we also have $p^2\mid N$. Let $k\geq 3$. Can the product of any $k$ consecutive positive integers ever be powerful? | Erdős Problems (#137, https://www.erdosproblems.com/137). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.137). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/137",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"powerful"
] | null | null | null | null | https://www.erdosproblems.com/137 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,951 | EP-138 | Erdős Problem #138 | Let the van der Waerden number $W(k)$ be such that whenever $N\geq W(k)$ and $\{1,\ldots,N\}$ is $2$-coloured there must exist a monochromatic $k$-term arithmetic progression. Improve the bounds for $W(k)$ - for example, prove that $W(k)^{1/k}\to \infty$. | Erdős Problems (#138, https://www.erdosproblems.com/138). Maintainer status: OPEN. Erdős prize: $500. OEIS: A005346. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.138). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/138",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics"
] | null | null | null | null | https://www.erdosproblems.com/138 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,952 | EP-141 | Erdős Problem #141 | Let $k\geq 3$. Are there $k$ consecutive primes in arithmetic progression? | Erdős Problems (#141, https://www.erdosproblems.com/141). Maintainer status: OPEN. OEIS: A006560. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.141). | 3 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | [
"GUY-A6"
] | {
"source_url": "https://www.erdosproblems.com/141",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"primes",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/141 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,953 | EP-142 | Erdős Problem #142 | Let $r_k(N)$ be the largest possible size of a subset of $\{1,\ldots,N\}$ that does not contain any non-trivial $k$-term arithmetic progression. Prove an asymptotic formula for $r_k(N)$. | Erdős Problems (#142, https://www.erdosproblems.com/142). Maintainer status: OPEN. Erdős prize: $10000. OEIS: A003002, A003003, A003004, A003005. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.142). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/142",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"arithmetic-progressions"
] | null | null | null | null | https://www.erdosproblems.com/142 | Erdős Problems (erdosproblems.com) | $10000 | [] | null | null | null | null | null | null | null | null | null | null |
1,954 | EP-143 | Erdős Problem #143 | Let $A\subset (1,\infty)$ be a countably infinite set such that for all $x\neq y\in A$ and integers $k\geq 1$ we have\[ \lvert kx -y\rvert \geq 1.\]Does this imply that $A$ is sparse? In particular, does this imply that\[\sum_{x\in A}\frac{1}{x\log x}<\infty\]or\[\sum_{\substack{x <n\\ x\in A}}\frac{1}{x}=o(\log n)?\] | Erdős Problems (#143, https://www.erdosproblems.com/143). Maintainer status: OPEN. Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.143). | 1 | partially_solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/143",
"checked_at": "2026-10-16",
"kind": "partial",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"primitive-sets"
] | null | null | null | null | https://www.erdosproblems.com/143 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,955 | EP-145 | Erdős Problem #145 | Let $s_1<s_2<\cdots$ be the sequence of squarefree numbers. Is it true that, for any $\alpha \geq 0$,\[\lim_{x\to \infty}\frac{1}{x}\sum_{s_n\leq x}(s_{n+1}-s_n)^\alpha\]exists? | Erdős Problems (#145, https://www.erdosproblems.com/145). Maintainer status: OPEN. OEIS: A005117. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.145). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/145",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory"
] | null | null | null | null | https://www.erdosproblems.com/145 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,956 | EP-146 | Erdős Problem #146 | If $H$ is bipartite and is $r$-degenerate, that is, every induced subgraph of $H$ has minimum degree $\leq r$, then\[\mathrm{ex}(n;H) \ll n^{2-1/r}.\] | Erdős Problems (#146, https://www.erdosproblems.com/146). Maintainer status: DISPROVED (LEAN). Erdős prize: $500. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.146). | 1 | solved | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/146",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "disproved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"graph-theory",
"turan-number"
] | The maintained Erdős Problems source lists problem 146 as “disproved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/146",
"label": "Erdős Problems #146: disproved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://hug... | 2026-09-27T00:00:00 | Erdős Problems #146: disproved (Lean): https://www.erdosproblems.com/146
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/146 | Erdős Problems (erdosproblems.com) | $500 | [] | null | null | null | null | null | null | null | null | null | null |
1,957 | EP-148 | Erdős Problem #148 | Let $F(k)$ be the number of solutions to\[ 1= \frac{1}{n_1}+\cdots+\frac{1}{n_k},\]where $1\leq n_1<\cdots<n_k$ are distinct integers. Find good estimates for $F(k)$. | Erdős Problems (#148, https://www.erdosproblems.com/148). Maintainer status: OPEN. OEIS: A076393, A006585. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.148). | 1 | open | null | null | 1 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/148",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"number-theory",
"unit-fractions"
] | null | null | null | null | https://www.erdosproblems.com/148 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,958 | EP-149 | Erdős Problem #149 | The strong chromatic index of a graph $G$, denoted by $\mathrm{sq}(G)$, is the minimum $k$ such that the edges of $G$ can be partitioned into $k$ sets of 'strongly independent' edges, that is, such that the subgraph of $G$ induced by each set is the union of vertex-disjoint edges.
Is it true that, for any graph $G$ wi... | Erdős Problems (#149, https://www.erdosproblems.com/149). Maintainer status: OPEN. | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/149",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/149 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,959 | EP-151 | Erdős Problem #151 | For a graph $G$ let $\tau(G)$ denote the minimal number of vertices that include at least one from each maximal clique of $G$ on at least two vertices (sometimes called the clique transversal number).
Let $H(n)$ be maximal such that every triangle-free graph on $n$ vertices contains an independent set on $H(n)$ vertic... | Erdős Problems (#151, https://www.erdosproblems.com/151). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.151). | 1 | open | null | null | 3 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 3,
"name": "graph_theory",
"display_name": "Graph Theory",
"description": "Problems involving graphs, networks, and their properties.",
"slug": "graph-theory",
"order_index": 3,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/151",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"graph-theory"
] | null | null | null | null | https://www.erdosproblems.com/151 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,960 | EP-152 | Erdős Problem #152 | For any $M\geq 1$, if $A\subset \mathbb{N}$ is a sufficiently large finite Sidon set then there are at least $M$ many $a\in A+A$ such that $a+1,a-1\not\in A+A$. | Erdős Problems (#152, https://www.erdosproblems.com/152). Maintainer status: PROVED (LEAN). Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.152). | 1 | solved | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2026-09-27T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/152",
"checked_at": "2026-10-16",
"kind": "resolution",
"evidence": "maintained_source",
"maintainer_status": "proved (Lean)"
} | null | null | null | null | [
"erdos-problems",
"sidon-sets"
] | The maintained Erdős Problems source lists problem 152 as “proved (Lean)” on 2026-09-27. The source marks a Lean verification of the resolution.
**What remains.** No unresolved part of the stated question is identified in the cited result. | [
{
"url": "https://www.erdosproblems.com/152",
"label": "Erdős Problems #152: proved (Lean)"
},
{
"url": "https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml",
"label": "Erdős Problems machine-readable status list (snapshot checked 2026-09-27)"
},
{
"url": "https://huggin... | 2026-09-27T00:00:00 | Erdős Problems #152: proved (Lean): https://www.erdosproblems.com/152
Erdős Problems machine-readable status list (snapshot checked 2026-09-27): https://github.com/teorth/erdosproblems/blob/main/data/problems.yaml | https://www.erdosproblems.com/152 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,961 | EP-153 | Erdős Problem #153 | Let $A$ be a finite Sidon set and $A+A=\{s_1<\cdots<s_t\}$. Is it true that\[\frac{1}{t}\sum_{1\leq i<t}(s_{i+1}-s_i)^2 \to \infty\]as $\lvert A\rvert\to \infty$? | Erdős Problems (#153, https://www.erdosproblems.com/153). Maintainer status: OPEN. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.153). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/153",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/153 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,962 | EP-155 | Erdős Problem #155 | Let $F(N)$ be the size of the largest Sidon subset of $\{1,\ldots,N\}$. Is it true that for every $k\geq 1$ we have\[F(N+k)\leq F(N)+1\]for all sufficiently large $N$? | Erdős Problems (#155, https://www.erdosproblems.com/155). Maintainer status: OPEN. OEIS: A143824, A227590, A003022. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.155). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/155",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"additive-combinatorics",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/155 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
1,963 | EP-156 | Erdős Problem #156 | Does there exist a maximal Sidon set $A\subset \{1,\ldots,N\}$ of size $O(N^{1/3})$? | Erdős Problems (#156, https://www.erdosproblems.com/156). Maintainer status: OPEN. OEIS: A382397. Formalized in Lean (google-deepmind/formal-conjectures, ErdosProblems.156). | 1 | open | null | null | 2 | 8 | 0 | 0 | 2024-01-01T00:00:00 | 2024-01-01T00:00:00 | true | {
"id": 2,
"name": "combinatorics",
"display_name": "Combinatorics",
"description": "Counting problems, graph theory, discrete structures.",
"slug": "combinatorics",
"order_index": 2,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 1,
"level": 1,
"name": "L1: Tractable",
"description": "Problems that may be within reach with current techniques. Reserved for future additions.",
"color_class": "text-green-600 bg-green-50 border-green-200"
} | {
"id": 8,
"name": "erdos_problems",
"display_name": "Erdős Problems",
"description": "A collection of open problems posed by Paul Erdős, one of the most prolific mathematicians of the 20th century. These problems span combinatorics, number theory, graph theory, and analysis.",
"slug": "erdos-problems",
"or... | null | {
"source_url": "https://www.erdosproblems.com/156",
"checked_at": "2026-10-16",
"kind": "open",
"evidence": "maintained_source",
"maintainer_status": "open"
} | null | null | null | null | [
"erdos-problems",
"sidon-sets"
] | null | null | null | null | https://www.erdosproblems.com/156 | Erdős Problems (erdosproblems.com) | null | [] | null | null | null | null | null | null | null | null | null | null |
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