id stringlengths 6 8 | alias stringlengths 24 50 | problem stringlengths 24 5.03k | answer int64 -16,384 80.2B | graph stringlengths 0 6.44k | domain stringclasses 4
values | secondary_domain stringclasses 4
values | goal stringclasses 4
values | evaluator_id stringclasses 1
value | root_lemma stringclasses 89
values | lemma_paths listlengths 0 5 | recipe_id stringlengths 0 6 | seed_template_id stringclasses 96
values | ending_id stringclasses 13
values | olympiad_level int64 2 9 | num_spawns int64 0 3 ⌀ | lemma_set listlengths 1 7 ⌀ | num_lemmas int64 1 7 ⌀ | generation_time float64 0 43.9 | created_at stringlengths 27 27 | verification dict | problem_hash stringlengths 6 6 | parent_id stringlengths 0 6 | variant stringclasses 3
values | license stringclasses 1
value | llm_solvers listlengths 1 13 ⌀ | solution_status int64 0 2 ⌀ | lemma_applicability listlengths 0 12 | irt_difficulty dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9eed90 | algebra_poly_eval_v1_1431428450_25 | Let $m = 16$. Let $T$ be the set of all integers $t$ such that $28 \leq t \leq 58$ and there exist integers $a$ and $b$ with $1 \leq a \leq 3$, $1 \leq b \leq 3$, and $t = 9a + 6b + 13$. Let $c = |T|$, the number of elements in $T$.
Compute the value of
$$
m^4 - 4m^3 + c \cdot m^2 - 2m - 5.
$$ | 51,419 | graphs = [
Graph(
let={
"m": Const(16),
"result": Sum(Pow(Ref("m"), Const(4)), Mul(Const(-4), Pow(Ref("m"), Const(3))), Mul(CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | algebra_poly_eval_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T13:08:12.142534Z | {
"verified": true,
"answer": 51419,
"timestamp": "2026-02-08T13:08:12.145800Z"
} | caf102 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 173,
"completion_tokens": 970
},
"timestamp": "2026-02-15T11:03:26.175Z",
"answer": 51419
},
{... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
294b69 | comb_binomial_compute_v1_1440796553_268 | Let $n$ be the smallest integer greater than or equal to $2$ that divides $709631$. Compute $\binom{n}{5}$. Multiply this value by $44121$, and compute the remainder when the result is divided by $95576$. Find this remainder. | 11,583 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(709631))))),
"k": Const(5),
"result": Binom(n=Ref("n"), k=Ref("k")),
"Q": Mod(va... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_binomial_compute_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T11:42:04.535209Z | {
"verified": true,
"answer": 11583,
"timestamp": "2026-02-08T11:42:04.536469Z"
} | 5147cc | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 102,
"completion_tokens": 927
},
"timestamp": "2026-02-14T17:41:09.942Z",
"answer": 11583
},
{... | 1 | [
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
58c8f1 | lin_form_endings_v1_1742523217_373 | Let $a = 56$, $b = 24$, $A = 20$, and $B = 17$. Let $g = \gcd(a, b)$. Define $$
= \left\lfloor \frac{aA + bB - a - b}{g} \right\rfloor + 1.$$Let $k = 11206$ and let $M = 94474$. Compute the remainder when $k \cdot n$ is divided by $M$. | 55,538 | graphs = [
Graph(
let={
"a_coeff": Const(56),
"b_coeff": Const(24),
"A_val": Const(20),
"B_val": Const(17),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T03:00:09.986120Z | {
"verified": true,
"answer": 55538,
"timestamp": "2026-02-08T03:00:09.986971Z"
} | 6ac551 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 215,
"completion_tokens": 752
},
"timestamp": "2026-02-09T17:09:36.622Z",
"answer": 55538
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"st... | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
024f0f | nt_count_gcd_equals_v1_1918700295_267 | Let $k = 49$ and $d = \phi(2)$, where $\phi$ denotes Euler's totient function. Determine the number of positive integers $n$ from 1 to 18496, inclusive, such that $\gcd(n, k) = d$. | 15,854 | graphs = [
Graph(
let={
"upper": Const(18496),
"k": Const(49),
"d": EulerPhi(n=Const(2)),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(GCD(a=Var("n"), b=Ref("k")), Ref("d"))))),
... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"ONE_PHI_2"
] | e19278 | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"ONE_PHI_2"
] | 2 | 7.713 | 2026-02-08T03:08:00.590979Z | {
"verified": true,
"answer": 15854,
"timestamp": "2026-02-08T03:08:08.303533Z"
} | eb63f0 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 357
},
"timestamp": "2026-02-17T19:49:52.714Z",
"answer": 15854
}
] | 2 | [
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "ONE_PHI_2",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
52a383 | comb_catalan_compute_v1_1918700295_3382 | Let $T$ be the set of all positive integers $t$ such that $5 \leq t \leq 16$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 5$, and $t = 3a + 2b$. Let $n$ be the number of elements in $T$. Compute the $n$-th Catalan number, denoted $C_n$. Find the remainder when $44121 \cdot C_n$ i... | 28,090 | graphs = [
Graph(
let={
"_n": Const(93718),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Va... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.003 | 2026-02-08T08:35:50.711158Z | {
"verified": true,
"answer": 28090,
"timestamp": "2026-02-08T08:35:50.714262Z"
} | 0c66ea | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 237,
"completion_tokens": 6400
},
"timestamp": "2026-02-24T09:43:48.027Z",
"answer": 28090
},
{
"... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
4524e5_n | alg_sum_ap_v1_1218484723_4752 | A biologist observes a colony of bacteria that reproduces in cycles. The number of reproduction cycles observed is equal to the number of primes between 2 and 1663 inclusive. In cycle $k$ (starting from $k=0$), $12k + 54$ new cells are produced. After all cycles, the total number of new cells is divided among 9466 petr... | 7,936 | ALG | null | COMPUTE | sympy | COUNT_PRIMES | [
"COUNT_PRIMES"
] | 07c874 | alg_sum_ap_v1 | null | 3 | null | [
"COUNT_PRIMES"
] | 1 | 0.004 | 2026-02-25T06:24:18.079239Z | null | 73fb70 | 4524e5 | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 199,
"completion_tokens": 32768
},
"timestamp": "2026-03-30T22:20:21.553Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": 3.8,
"mid": 6.33,
"hi": 9.49
} | |
7f03d2 | antilemma_k3_v1_1978505735_1221 | Let $x = \sum_{d \mid 22831} \phi(d)$, where $\phi$ denotes Euler's totient function. Let $A = \sum_{d_1 \mid \left(\sum_{d_2 \mid 2003} \phi(d_2)\right)} \phi(d_1)$. Compute the remainder when $x \bmod 317 + A \cdot (x \bmod 313)$ is divided by $59445$. | 55,887 | graphs = [
Graph(
let={
"_m": Const(2003),
"_n": Const(313),
"x": SumOverDivisors(n=Const(value=22831), var='d', expr=EulerPhi(n=Var(name='d'))),
"Q": Mod(value=Sum(Mod(value=Ref("x"), modulus=Const(317)), Mul(SumOverDivisors(n=SumOverDivisors(n=Ref(name='_m')... | NT | COMB | COMPUTE | sympy | K13 | [
"K3/K3",
"K3"
] | 8c95c7 | antilemma_k3_v1 | two_moduli | 5 | 0 | [
"K13",
"K3"
] | 2 | 0.008 | 2026-02-08T15:58:33.160462Z | {
"verified": true,
"answer": 55887,
"timestamp": "2026-02-08T15:58:33.168387Z"
} | 6cca33 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 881
},
"timestamp": "2026-02-16T18:00:40.921Z",
"answer": 55887
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a91588 | sequence_count_fib_divisible_v1_1918700295_2449 | Let $T$ be the set of all integers $t$ such that $21 \leq t \leq 507$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 31$, $1 \leq b \leq 15$, and $t = 12a + 9b$. Let $d = 6$. Determine the number of positive integers $n$ such that $1 \leq n \leq |T|$ and $d$ divides the $n$-th Fibonacci number. | 13 | graphs = [
Graph(
let={
"upper": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=31)), Geq(left=Var(name='b'), right=Const(va... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.009 | 2026-02-08T07:53:14.091696Z | {
"verified": true,
"answer": 13,
"timestamp": "2026-02-08T07:53:14.100791Z"
} | daffea | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 159,
"completion_tokens": 3332
},
"timestamp": "2026-02-13T13:11:42.290Z",
"answer": 13
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
ab1185 | comb_binomial_compute_v1_784195855_3957 | Let $n = 13$ and let $k$ be the largest prime number satisfying $2 \leq k \leq 6$. Compute $\binom{n}{k}$. | 1,287 | graphs = [
Graph(
let={
"_n": Const(6),
"n": Const(13),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"result": Binom(n=Ref("n"), k=Ref("k")),
},
goal=Ref("... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | comb_binomial_compute_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.002 | 2026-02-08T06:42:57.158077Z | {
"verified": true,
"answer": 1287,
"timestamp": "2026-02-08T06:42:57.159984Z"
} | 8a2914 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 93,
"completion_tokens": 569
},
"timestamp": "2026-02-15T17:43:15.528Z",
"answer": 1287
},
{
"id": 11,
... | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status":... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
5c08b2 | geo_count_lattice_rect_v1_865884756_259 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 34$ and $0 \leq y \leq 135$. | 4,760 | graphs = [
Graph(
let={
"a": Const(34),
"b": Const(135),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 2 | 0 | null | null | 0.002 | 2026-02-08T15:17:16.211604Z | {
"verified": true,
"answer": 4760,
"timestamp": "2026-02-08T15:17:16.213550Z"
} | b0c8a8 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 148,
"completion_tokens": 132
},
"timestamp": "2026-02-10T06:13:47.641Z",
"answer": 4760
},
{
"id... | 1 | [] | {
"lo": -8.52,
"mid": -5.43,
"hi": -3.2
} | ||||
a2ad05 | nt_num_divisors_compute_v1_1742523217_4800 | Let $n$ be the number of integers $t$ such that $16 \leq t \leq 51$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 6$, $1 \leq b \leq 6$, and $t = 3a + 4b + 9$. Compute the number of positive divisors of $n$. | 8 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=6)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_num_divisors_compute_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T09:08:16.971184Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T09:08:16.972902Z"
} | 921446 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 129,
"completion_tokens": 2217
},
"timestamp": "2026-02-14T02:36:28.740Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
cc0616 | nt_count_with_divisor_count_v1_124444284_8818 | Let $d$ be the sum $1 + 2 + 3 + 4$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 59536$ and the number of positive divisors of $n$ is equal to $d$. Let $r$ be the number of elements in $S$. Compute the remainder when $44121 \cdot r$ is divided by $97693$. | 45,199 | graphs = [
Graph(
let={
"_n": Const(97693),
"upper": Const(59536),
"div_count": Summation(var="k", start=Const(1), end=Const(4), expr=Var("k")),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upp... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | nt_count_with_divisor_count_v1 | null | 4 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 4.094 | 2026-02-08T11:55:13.965604Z | {
"verified": true,
"answer": 45199,
"timestamp": "2026-02-08T11:55:18.060065Z"
} | 1250d9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 3335
},
"timestamp": "2026-02-14T20:33:50.073Z",
"answer": 45199
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
abeab6 | comb_count_surjections_v1_124444284_2894 | Let $m$ be the number of integers $t$ such that $5 \leq t \leq 14$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 4$, and $t = 3a + 2b$. Let $n$ be the number of ordered pairs $(i, j)$ with $1 \leq i \leq 6$, $1 \leq j \leq 7$, and $i + j = m$. Compute $6! \cdot S(n, 6)$, where $S(... | 720 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS"
] | 8a3f7a | comb_count_surjections_v1 | null | 6 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.02 | 2026-02-08T05:03:43.671505Z | {
"verified": true,
"answer": 720,
"timestamp": "2026-02-08T05:03:43.691898Z"
} | 2c8e51 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 265,
"completion_tokens": 1059
},
"timestamp": "2026-02-11T22:48:42.588Z",
"answer": 720
},
{
"id... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok_later"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
... | {
"lo": -5.97,
"mid": -3.96,
"hi": -1.93
} | ||
9fe6a1 | antilemma_sum_primes_v1_1874849503_955 | Let $m = 33075$. Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 72$, $\gcd(p, q) = 1$, and $p < q$. Let $S$ be the set of all prime numbers $n$ satisfying $n \geq n$ and $n \leq d$, where $d$ is the smallest divisor of $m$ that is at least $n$. Compute the s... | 5 | graphs = [
Graph(
let={
"_m": Const(33075),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR/SUM_PRIMES",
"COPRIME_PAIRS/SUM_PRIMES",
"SUM_PRIMES"
] | ba4bc1 | antilemma_sum_primes_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR",
"SUM_PRIMES"
] | 3 | 0.013 | 2026-02-08T13:27:17.961428Z | {
"verified": true,
"answer": 5,
"timestamp": "2026-02-08T13:27:17.974556Z"
} | 0980f0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 1292
},
"timestamp": "2026-02-09T23:04:26.329Z",
"answer": 5
},
{
"id":... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_later"
},
{
"lemm... | {
"lo": -6.5,
"mid": -0.2,
"hi": 6.11
} | ||
6c0cb7 | comb_bell_compute_v1_1218484723_5576 | Let $B_n$ denote the $n$-th Bell number. Let $n$ be the number of integers $a$ with $0 \le a \le 4488$ such that
$$3\,(3a^{4} + a^{2} - 4a + 1 \bmod 4489)^{4} + (3a^{4} + a^{2} - 4a + 1 \bmod 4489)^{2} - 4\,(3a^{4} + a^{2} - 4a + 1 \bmod |\{t : \text{there exist integers } a,b \text{ with } 1 \le a \le 703,\ 1 \le b \l... | 14,085 | graphs = [
Graph(
let={
"_m": Const(3),
"_n": Const(3),
"n": CountOverSet(set=SolutionsSet(var=Var("a"), condition=And(Geq(Var("a"), Const(0)), Leq(Var("a"), Const(4488)), Eq(Mod(value=Sum(Mul(Const(3), Pow(Mod(value=Sum(Mul(Ref("_n"), Pow(Var("a"), Const(4))), Pow(Var("a... | COMB | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/POLY_ORBIT_HENSEL"
] | 007af8 | comb_bell_compute_v1 | null | 8 | 0 | [
"LIN_FORM",
"POLY_ORBIT_HENSEL"
] | 2 | 0.008 | 2026-02-25T07:04:38.277009Z | {
"verified": true,
"answer": 14085,
"timestamp": "2026-02-25T07:04:38.284712Z"
} | f8a38c | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 361,
"completion_tokens": 32768
},
"timestamp": "2026-03-29T21:47:30.712Z",
"answer": null
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_ORBIT_HE... | {
"lo": 3.81,
"mid": 6.33,
"hi": 9.49
} | ||
19d768 | comb_sum_binomial_row_v1_124444284_6062 | Let $n$ be the number of integers $t$ such that $7 \leq t \leq 22$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 6$, and $t = 5a + 2b$. Compute $2^n$. | 4,096 | graphs = [
Graph(
let={
"_n": Const(2),
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(na... | NT | null | SUM | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T08:06:30.386336Z | {
"verified": true,
"answer": 4096,
"timestamp": "2026-02-08T08:06:30.387635Z"
} | 416cad | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 133,
"completion_tokens": 628
},
"timestamp": "2026-02-15T19:41:41.604Z",
"answer": 65536
},
{
"id": 11... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.34
} | ||
f8a715 | comb_sum_binomial_row_v1_1520064083_9827 | Let $ m = 2 $ and $ n = 2 $. Let $ k $ be the largest prime number satisfying $ m \leq k \leq \sum_{i=1}^{5} i $. Compute $ n^k $. | 8,192 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(2),
"n": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Summation(var="k", start=Const(1), end=Const(5), expr=Var("k"))), IsPrime(Var("n"))))),
"result": Pow(R... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | bde608 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T11:01:01.682328Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T11:01:01.684341Z"
} | 9f4662 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 103,
"completion_tokens": 332
},
"timestamp": "2026-02-15T21:07:09.438Z",
"answer": 8192
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V1",
"status": "no"
},
{... | {
"lo": -10,
"mid": -7.71,
"hi": -5.43
} | ||
3ac88b | nt_count_primes_v1_1978505735_3852 | Let $S$ be the set of all positive integers $n_1$ such that $1 \leq n_1 \leq 3$ and $\gcd(n_1, 10) = 1$. Let $k$ be the number of elements in $S$. Determine the number of prime numbers $n$ such that $k \leq n \leq 11131$. | 1,349 | graphs = [
Graph(
let={
"upper": Const(11131),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(3)), Eq(GCD(a=Var("n1"), b=Const(10)), Const(1)))... | NT | null | COUNT | sympy | C4 | [
"C4"
] | 08d162 | nt_count_primes_v1 | null | 4 | 0 | [
"C4"
] | 1 | 0.246 | 2026-02-08T17:54:17.556445Z | {
"verified": true,
"answer": 1349,
"timestamp": "2026-02-08T17:54:17.802240Z"
} | 64a90c | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 126,
"completion_tokens": 2406
},
"timestamp": "2026-02-18T09:22:51.110Z",
"answer": 1349
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
db57be_n | geo_count_lattice_triangle_v1_1218484723_1175 | A game board has positions labeled by pairs $(a,b)$ with $a,b$ from 1 to 5. Each position has a score given by $337a^4 - 512a^3b + 384a^2b^2 - 128ab^3 + 16b^4$. Let $M$ be the lowest score on the board. Separately, a player earns bonus points: $R = |11100 - 3969|$, and combines gcd-based modifiers involving 100, 81, 49... | 3,564 | GEOM | null | COUNT | sympy | POLY4_MIN | [
"POLY4_MIN/B1"
] | f72039 | geo_count_lattice_triangle_v1 | null | 6 | null | [
"B1",
"POLY4_MIN"
] | 2 | 0.01 | 2026-02-25T02:56:06.022935Z | null | 9696b8 | db57be | narrative | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 268,
"completion_tokens": 16310
},
"timestamp": "2026-03-30T16:28:24.264Z",
"answer": 3563
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "POLY4_MIN",
"status": "ok"
}
] | {
"lo": 1.5,
"mid": 4.69,
"hi": 7.23
} | |
80aa1f | comb_sum_binomial_row_v1_1218484723_6888 | Let $n$ be the number of ordered pairs $(a, b)$ of positive integers with $1 \le a, b \le 30$ such that $16a^2 - 8ab + b^2 = 225$. Let $R = 2^n$. Find the remainder when $13879R$ is divided by $59240$. | 48,232 | graphs = [
Graph(
let={
"_n": Const(30),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(30)), Geq(Var("b"), Const(1)), Leq(Var("b"), Ref("_n")), Eq(Sum(Mul(Const(-8), Var("a"), Var("b")), Pow(Var... | COMB | null | SUM | sympy | QF_PSD_COUNT | [
"QF_PSD_COUNT"
] | 09ce67 | comb_sum_binomial_row_v1 | null | 5 | 0 | [
"QF_PSD_COUNT"
] | 1 | 0.002 | 2026-02-25T08:20:27.671053Z | {
"verified": true,
"answer": 48232,
"timestamp": "2026-02-25T08:20:27.672553Z"
} | 6dc5c9 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 5723
},
"timestamp": "2026-03-30T03:01:22.986Z",
"answer": 48232
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT",
"status": "ok"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
... | {
"lo": -3.33,
"mid": 1.03,
"hi": 5.26
} | ||
1e8195 | comb_count_derangements_v1_349078426_1677 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p \cdot q = 5250$, $\gcd(p, q) = 1$, and $p < q$. Let $\text{result} = !n$, the subfactorial of $n$. Compute $\text{result}$. | 14,833 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=5250)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q')), right=Const(value=1)),... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.002 | 2026-02-08T13:50:51.432487Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T13:50:51.434007Z"
} | 701b4a | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 122,
"completion_tokens": 2470
},
"timestamp": "2026-02-15T20:52:09.628Z",
"answer": 14833
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
daad19 | nt_sum_divisors_mod_v1_1820931509_337 | Let $\sigma$ be the sum of the positive divisors of 15120. Let $r$ be the remainder when $\sigma$ is divided by 11311. Let $C$ be the number of positive integers $k$ at most 51561 such that $153$ divides $k$. Compute the remainder when $\left(r \bmod 293\right) + 1009 \cdot \left(r \bmod C\right)$ is divided by 57098. | 43,064 | graphs = [
Graph(
let={
"_n": Const(51561),
"n": Const(15120),
"M": Const(11311),
"sigma": SumDivisors(n=Ref("n")),
"result": Mod(value=Ref("sigma"), modulus=Ref("M")),
"_c": Const(1009),
"Q": Mod(value=Sum(Mod(value=Ref("re... | NT | null | COMPUTE | sympy | C2 | [
"C2"
] | 580f49 | nt_sum_divisors_mod_v1 | two_moduli | 5 | 0 | [
"C2"
] | 1 | 0.002 | 2026-02-08T11:30:35.320330Z | {
"verified": true,
"answer": 43064,
"timestamp": "2026-02-08T11:30:35.321874Z"
} | a74878 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 1396
},
"timestamp": "2026-02-14T15:53:38.560Z",
"answer": 43064
},
... | 1 | [
{
"lemma": "C2",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
a71f70 | antilemma_sum_factor_cartesian_v1_2080023795_145 | Let $n = 90$. Let $d_{\text{min}}$ be the smallest integer $d \geq 2$ that divides $n$. Let $T$ be the set of all ordered pairs $(i, j)$ where $i$ is an integer from 1 to 22 and $j$ is an integer from 1 to 21. Let $x$ be the sum of $i \cdot j$ over all pairs $(i, j)$ in $T$. Let $m = |x| + 2$. The Fibonacci entry point... | 7,305 | graphs = [
Graph(
let={
"_n": Const(90),
"x": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=EulerPhi(n=MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Ref("_n")))))), ... | NT | null | COMPUTE | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/ONE_PHI_2/SUM_FACTOR_CARTESIAN",
"SUM_FACTOR_CARTESIAN"
] | 1d308a | antilemma_sum_factor_cartesian_v1 | null | 7 | 0 | [
"MIN_PRIME_FACTOR",
"ONE_PHI_2",
"SUM_FACTOR_CARTESIAN"
] | 3 | 0.002 | 2026-02-08T11:34:41.875425Z | {
"verified": true,
"answer": 7305,
"timestamp": "2026-02-08T11:34:41.877188Z"
} | dd6daf | CC BY 4.0 | [
{
"id": 4,
"model": "NousResearch/Hermes-4-405B",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 212,
"completion_tokens": 524
},
"timestamp": "2026-02-09T10:27:02.609Z",
"answer": 19485
},... | 0 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "ONE_PHI_2",
"status":... | {
"lo": -1.8,
"mid": 3.87,
"hi": 9.6
} | ||
512274 | antilemma_sum_equals_v1_1520064083_9892 | Let $m$ be the number of integers $t$ such that $5 \leq t \leq 130$ and there exist positive integers $a$ and $b$ with $1 \leq a \leq 4$, $1 \leq b \leq 59$, and $t = 3a + 2b$. Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = m$. Compute the number of ordered pairs $(i... | 59 | graphs = [
Graph(
let={
"_m": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=4)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"LIN_FORM/COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | b14821 | antilemma_sum_equals_v1 | null | 6 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 3 | 0.099 | 2026-02-08T11:02:13.529633Z | {
"verified": true,
"answer": 59,
"timestamp": "2026-02-08T11:02:13.628844Z"
} | 5daf69 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 270,
"completion_tokens": 9748
},
"timestamp": "2026-02-24T12:45:19.977Z",
"answer": 59
},
{
"id"... | 1 | [
{
"lemma": "COMB1",
"status": "ok_later"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
9879b9 | algebra_poly_eval_v1_717093673_3529 | Let $a$ be the largest prime number $n$ such that $2 \leq n \leq 30$. Compute $2a^2 + 9a + 3$. | 1,946 | graphs = [
Graph(
let={
"_n": Const(9),
"a": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), Const(30)), IsPrime(Var("n"))))),
"result": Sum(Mul(Const(2), Pow(Ref("a"), Const(2))), Mul(Ref("_n"), Ref("a")), Const(3)),
... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW"
] | dc3ad3 | algebra_poly_eval_v1 | null | 2 | 0 | [
"MAX_PRIME_BELOW"
] | 1 | 0.003 | 2026-02-08T17:39:40.262677Z | {
"verified": true,
"answer": 1946,
"timestamp": "2026-02-08T17:39:40.265373Z"
} | d6296d | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 94,
"completion_tokens": 329
},
"timestamp": "2026-02-16T11:30:18.362Z",
"answer": 1946
},
{
"id": 11,
... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -10,
"mid": -7.27,
"hi": -4.54
} | ||
f8fbdf | sequence_lucas_compute_v1_124444284_3413 | Let $n$ be the sum of all even integers from $1$ to $8$ inclusive. Compute the $n$-th Lucas number. | 15,127 | graphs = [
Graph(
let={
"_n": Const(2),
"n": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(8)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
"result": Lucas(arg=Ref(name='n')),
},
goal=Ref(... | NT | null | COMPUTE | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | sequence_lucas_compute_v1 | null | 3 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 0.001 | 2026-02-08T05:23:46.103901Z | {
"verified": true,
"answer": 15127,
"timestamp": "2026-02-08T05:23:46.104678Z"
} | d814b5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 742
},
"timestamp": "2026-02-12T07:41:35.358Z",
"answer": 15127
},
{
... | 1 | [
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
b65b8f | nt_sum_phi_v1_1125832087_1434 | Let $N$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that
$$pq=24,\quad \gcd(p,q)=1,\quad p<q.$$
Let $\text{upper}$ be the maximum value of $xy$ over all ordered pairs $(x,y)$ of positive integers such that
$$x+y=46.$$
Let $\text{result}$ be the sum of $\varphi(n)$ over al... | 1 | graphs = [
Graph(
let={
"_m": Const(26741),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/B1/MIN_PRIME_FACTOR"
] | e8368f | nt_sum_phi_v1 | bell_mod | 7 | 0 | [
"B1",
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 3 | 0.032 | 2026-02-08T03:44:28.795931Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T03:44:28.827815Z"
} | 0c07fe | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 251,
"completion_tokens": 4137
},
"timestamp": "2026-02-11T17:26:19.080Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok_... | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ddfce4 | nt_min_crt_v1_397696148_1351 | Let $m = 7$. Let $k$ be the largest positive integer such that the number of ordered pairs $(p, q)$ of positive integers satisfying $pq = 72$, $\gcd(p, q) = 1$, and $p < q$ raised to the power $k$ is at most $524$. Let $a = 6$ and $b = 7$. Find the smallest positive integer $n \leq 63$ such that $n \equiv a \pmod{m}$ a... | 64,250 | graphs = [
Graph(
let={
"m": Const(7),
"k": MaxOverSet(set=SolutionsSet(var=Var("k"), condition=Leq(Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Co... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_VAL"
] | aa93c6 | nt_min_crt_v1 | null | 7 | 0 | [
"COPRIME_PAIRS",
"MAX_VAL"
] | 2 | 0.008 | 2026-02-08T12:31:19.004195Z | {
"verified": true,
"answer": 64250,
"timestamp": "2026-02-08T12:31:19.011891Z"
} | 09d4ae | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 188,
"completion_tokens": 1767
},
"timestamp": "2026-02-15T01:32:34.502Z",
"answer": 64250
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "ok_later"
},
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
790167 | nt_sum_totient_over_divisors_v1_1918700295_35 | Let $n$ be the minimum value of $x + y$ over all pairs of positive integers $(x,y)$ such that $xy = 3751969$.
Let $R = \sum_{d \mid n} \phi(d)$, where $\phi$ is Euler's totient function.
Let $Q$ be the remainder when $63345 \cdot R$ is divided by $54056$.
Compute $Q$. | 38,346 | graphs = [
Graph(
let={
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(3751969)))), expr=Sum(Var("x"), Var("y")))),
"result": SumOv... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | nt_sum_totient_over_divisors_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.003 | 2026-02-08T02:57:31.185856Z | {
"verified": true,
"answer": 38346,
"timestamp": "2026-02-08T02:57:31.188751Z"
} | 7b47df | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 201,
"completion_tokens": 4676
},
"timestamp": "2026-02-10T12:03:01.449Z",
"answer": 38346
},
{
"... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -3.55,
"mid": 0.8,
"hi": 4.81
} | ||
74cdd4 | comb_count_derangements_v1_1125832087_739 | Let $n$ be the number of integers $k$ such that $1 \leq k \leq 24$ and $$k \equiv \left\lfloor \frac{k}{2} \right\rfloor \pmod{3}.$$ Compute the subfactorial of $n$, denoted $!n$. Enter your answer as an integer between 0 and 99999. | 14,833 | graphs = [
Graph(
let={
"_n": Const(24),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modulus=Const(value=3))))),
"r... | NT | COMB | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | comb_count_derangements_v1 | null | 5 | 0 | [
"L3C"
] | 1 | 0.001 | 2026-02-08T03:14:45.326481Z | {
"verified": true,
"answer": 14833,
"timestamp": "2026-02-08T03:14:45.327336Z"
} | ec7831 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 194,
"completion_tokens": 888
},
"timestamp": "2026-02-10T13:33:46.249Z",
"answer": 14833
},
{
"i... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.92,
"mid": -3.15,
"hi": 0.25
} | ||
e398b3 | nt_max_prime_below_v1_1520064083_8382 | Let $ T $ be the set of all ordered pairs $ (x, y) $ of positive integers such that $ xy = 1600 $. Let $ m $ be the minimum value of $ x + y $ as $ (x, y) $ ranges over $ T $. Let $ K $ be the number of positive integers $ k \leq 160 $ such that $ m $ divides $ k $. Let $ N $ be the largest prime number at most $ 42849... | 42,841 | graphs = [
Graph(
let={
"upper": Const(42849),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("k"), condition=And(Geq(Var("k"), Const(1)), Leq(Var("k"), Const(160)), Divides(divisor=MinOverSet(set=MapOverSet(set=S... | NT | null | EXTREMUM | sympy | B3 | [
"B3/C2"
] | dcbe93 | nt_max_prime_below_v1 | null | 6 | 0 | [
"B3",
"C2"
] | 2 | 1.096 | 2026-02-08T10:09:55.132088Z | {
"verified": true,
"answer": 42841,
"timestamp": "2026-02-08T10:09:56.228313Z"
} | 44c59f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2127
},
"timestamp": "2026-02-14T06:38:13.060Z",
"answer": 42841
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "C2",
"status": "ok_later"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
d41d99 | sequence_count_fib_divisible_v1_677425708_3881 | Let $d$ be the number of positive integers $n$ such that $1 \leq n \leq 109$ and $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{11}$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 929$ and $d$ divides $F_n$, where $F_n$ denotes the $n$-th Fibonacci number. Compute the remainder when $... | 58,903 | graphs = [
Graph(
let={
"_n": Const(85832),
"upper": Const(929),
"d": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(109)), Congruent(a=Var(name='n'), b=Floor(arg=Div(left=Var(name='n'), right=Const(value=2))), modul... | NT | null | COUNT | sympy | L3C | [
"L3C"
] | 73f8b0 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"L3C"
] | 1 | 0.114 | 2026-02-08T06:01:10.337432Z | {
"verified": true,
"answer": 58903,
"timestamp": "2026-02-08T06:01:10.451678Z"
} | 019397 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1820
},
"timestamp": "2026-02-12T18:30:36.748Z",
"answer": 58903
},
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
ef521a | lin_form_endings_v1_1915831931_245 | Let $a = 8$, $b = 12$, $A = 37$, and $B = 33$. Let $g = \gcd(a, b)$, and define $a' = \left\lfloor \frac{a}{g} \right\rfloor$ and $b' = \left\lfloor \frac{b}{g} \right\rfloor$. Compute the value of
$$
(13856 \cdot (a'A + b'B - a'b')) \mod 70702.
$$ | 51,488 | graphs = [
Graph(
let={
"a_coeff": Const(8),
"b_coeff": Const(12),
"A_val": Const(37),
"B_val": Const(33),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"ap_node": Floor(Div(Ref("a_coeff"), Ref("g_step"))),
"bp_node": F... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T15:17:01.651345Z | {
"verified": true,
"answer": 51488,
"timestamp": "2026-02-08T15:17:01.653704Z"
} | 6af7ed | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 153,
"completion_tokens": 708
},
"timestamp": "2026-02-16T04:05:04.130Z",
"answer": 51488
},
{... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dad78f | comb_catalan_compute_v1_1125832087_98 | Let $n$ be the number of positive integers $t$ such that there exist integers $a$ and $b$ satisfying $1 \leq a \leq 5$, $1 \leq b \leq 2$, $5 \leq t \leq 16$, and $t = 2a + 3b$.
Let $C_n$ be the $n$-th Catalan number. Define $S = |C_n| + 1$. Compute $C_n + \phi(S) + \tau(S)$, where $\phi(S)$ is the number of positive ... | 26,964 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=5)), Geq(left=Var(name='b'), right=Const(value=1... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_catalan_compute_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T02:52:10.311676Z | {
"verified": true,
"answer": 26964,
"timestamp": "2026-02-08T02:52:10.313336Z"
} | bee96b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 271,
"completion_tokens": 1953
},
"timestamp": "2026-02-10T11:42:48.269Z",
"answer": 26964
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": 0.04,
"mid": 1.71,
"hi": 3.18
} | ||
4ec8c9 | comb_count_derangements_v1_124444284_2989 | Let $m = 13013$. A positive integer $p$ is called special if there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $n$ be the smallest divisor of $m$ that is greater than or equal to the number of special integers. Compute the number of derangements of $n$ elements, denoted $!n$. | 1,854 | graphs = [
Graph(
let={
"_m": Const(13013),
"_n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=24)), Eq(left=GCD(a=Var(name='p'), b=Var(nam... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MIN_PRIME_FACTOR"
] | 52cee2 | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MIN_PRIME_FACTOR"
] | 2 | 0.001 | 2026-02-08T05:06:45.184824Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T05:06:45.186250Z"
} | 0ee322 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 204,
"completion_tokens": 2203
},
"timestamp": "2026-02-11T22:52:57.120Z",
"answer": 1854
},
{
"... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.33
} | ||
ad9217 | nt_max_prime_below_v1_151522320_1572 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 36$, $\gcd(p, q) = 1$, and $p < q$. Let $c$ be the number of elements in $P$. Determine the value of the largest prime number $n$ such that $c \le n \le 59049$. | 59,029 | graphs = [
Graph(
let={
"upper": Const(59049),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 5.696 | 2026-02-08T04:06:17.006322Z | {
"verified": true,
"answer": 59029,
"timestamp": "2026-02-08T04:06:22.702781Z"
} | 590442 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 4768
},
"timestamp": "2026-02-10T15:20:34.116Z",
"answer": 59029
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
945d75 | antilemma_sum_primes_v1_548369836_24 | Let $A$ be the set of all integers $t$ such that $33 \leq t \leq 567$ and there exist positive integers $a$, $b$ with $1 \leq a \leq 35$, $1 \leq b \leq 7$, and $t = 12a + 21b$. Let $N$ be the number of elements in $A$. Define $x$ to be the sum of all prime numbers $n$ such that $2 \leq n \leq N$. Compute the value of ... | 2,584 | graphs = [
Graph(
let={
"_n": Const(2),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"LIN_FORM/SUM_PRIMES",
"SUM_PRIMES"
] | 7e2259 | antilemma_sum_primes_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM",
"SUM_PRIMES"
] | 3 | 0.013 | 2026-02-08T02:42:54.543236Z | {
"verified": true,
"answer": 2584,
"timestamp": "2026-02-08T02:42:54.556579Z"
} | d1821a | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 233,
"completion_tokens": 5446
},
"timestamp": "2026-02-09T18:54:05.538Z",
"answer": 2584
},
{
"... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"... | {
"lo": 2.06,
"mid": 5.24,
"hi": 8.53
} | ||
de8bb9 | comb_count_partitions_v1_48377204_1946 | Let $m = 21$. Define $d$ to be the number of positive integers $n_1$ such that $1 \leq n_1 \leq 631$ and $\gcd(n_1, m) = 1$. Consider all ordered pairs $(x, y)$ of positive integers such that $xy = d$. Let $n$ be the minimum value of $x + y$ over all such pairs. Compute the number of integer partitions of $n$. | 26,015 | graphs = [
Graph(
let={
"_m": Const(21),
"_n": CountOverSet(set=SolutionsSet(var=Var("n1"), condition=And(Geq(Var("n1"), Const(1)), Leq(Var("n1"), Const(631)), Eq(GCD(a=Var("n1"), b=Ref("_m")), Const(1))))),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elemen... | NT | COMB | COUNT | sympy | C4 | [
"C4/B3"
] | 046ad7 | comb_count_partitions_v1 | null | 6 | 0 | [
"B3",
"C4"
] | 2 | 0.003 | 2026-02-08T16:31:11.818788Z | {
"verified": true,
"answer": 26015,
"timestamp": "2026-02-08T16:31:11.821933Z"
} | 18eca2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 1257
},
"timestamp": "2026-02-17T06:19:35.014Z",
"answer": 26015
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemm... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c5afba | diophantine_fbi2_count_v1_238844314_1068 | Let $k = 840$. Consider the set of all positive integers $d$ such that $6 \leq d \leq 118$, $d$ divides $k$, and
$$
6 \leq \frac{k}{d} \leq 117.
$$
Additionally, require that $\frac{k}{d} \geq m$, where $m$ is the smallest positive integer greater than or equal to $2$ that divides $6125$. Let $R$ be the number of such ... | 49,554 | graphs = [
Graph(
let={
"_n": Const(44121),
"k": Const(840),
"result": CountOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(6)), Leq(Var("d"), Const(118)), Divides(divisor=Var("d"), dividend=Ref("k")), Geq(Div(Ref("k"), Var("d")), MinOverSet(set=S... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | diophantine_fbi2_count_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.016 | 2026-02-08T13:53:03.398354Z | {
"verified": true,
"answer": 49554,
"timestamp": "2026-02-08T13:53:03.414150Z"
} | f363bf | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1642
},
"timestamp": "2026-02-15T21:28:33.804Z",
"answer": 49554
},
... | 1 | [
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "n... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
2a7248 | nt_euler_phi_compute_v1_260342960_152 | Let $n = 88888$. Define $r = \phi(n)$, where $\phi$ denotes Euler's totient function. Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x + y = 142$. Let $M$ be the maximum value of $xy$ over all pairs $(x, y) \in P$. Compute the remainder when $M - r$ is divided by $83983$. | 45,824 | graphs = [
Graph(
let={
"_n": Const(83983),
"n": Const(88888),
"result": EulerPhi(n=Ref("n")),
"Q": Mod(value=Sub(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=V... | NT | null | COMPUTE | sympy | B1 | [
"B1"
] | d2b6e1 | nt_euler_phi_compute_v1 | negation_mod | 5 | 0 | [
"B1"
] | 1 | 0.001 | 2026-02-08T11:16:41.526992Z | {
"verified": true,
"answer": 45824,
"timestamp": "2026-02-08T11:16:41.528009Z"
} | 1dbd56 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1085
},
"timestamp": "2026-02-10T02:27:52.560Z",
"answer": 45824
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
}... | {
"lo": -0.51,
"mid": 1.66,
"hi": 3.57
} | ||
d57c3e | modular_count_residue_v1_238844314_383 | Let $m$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 36$. Let $r$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = 6$. Let $N$ be the number of positive integers $n$ such that $1 \leq n \leq 32768$ and $n \equiv ... | 684 | graphs = [
Graph(
let={
"_m": Const(36),
"_n": Const(6),
"upper": Const(32768),
"m": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"... | NT | null | COUNT | sympy | B1 | [
"B1",
"B3"
] | 655d51 | modular_count_residue_v1 | null | 7 | 0 | [
"B1",
"B3"
] | 2 | 1.13 | 2026-02-08T13:18:38.497206Z | {
"verified": true,
"answer": 684,
"timestamp": "2026-02-08T13:18:39.627086Z"
} | 152d76 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 181,
"completion_tokens": 3118
},
"timestamp": "2026-02-15T13:03:37.180Z",
"answer": 684
},
{
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemm... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
c2d49e | lin_form_endings_v1_124444284_5700 | Let $a = 28$ and $b = 49$. Let $L$ be the least common multiple of $a$ and $b$. Define $s = 1 \cdot L + a + b$. Let $S = 10523 \cdot s$. Compute the remainder when $S$ is divided by $72668$. | 38,727 | graphs = [
Graph(
let={
"a_coeff": Const(28),
"b_coeff": Const(49),
"k_val": Const(1),
"lcm_node": LCM(a=Ref("a_coeff"), b=Ref("b_coeff")),
"_inner_result": Sum(Mul(Ref("k_val"), Ref("lcm_node")), Ref("a_coeff"), Ref("b_coeff")),
"_scal... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 2 | null | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T06:46:41.306946Z | {
"verified": true,
"answer": 38727,
"timestamp": "2026-02-08T06:46:41.308091Z"
} | 73b0f8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 117,
"completion_tokens": 2452
},
"timestamp": "2026-02-13T04:28:13.669Z",
"answer": 38727
},
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
4588a9 | nt_count_coprime_v1_865884756_3387 | Let $M$ be the number of positive integers $n$ with $1 \le n \le 1619$ such that $n \equiv \left\lfloor \frac{n}{2} \right\rfloor \pmod{5}$. Let $k$ be the largest positive divisor of $M$ that is at most $17$. Compute the number of positive integers $n_1$ such that $1 \le n_1 \le 27225$ and $\gcd(n_1, k) = 1$. | 25,624 | graphs = [
Graph(
let={
"upper": Const(27225),
"k": MaxOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(1)), Leq(Var("d"), Const(17)), Divides(divisor=Var("d"), dividend=CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var... | NT | null | COUNT | sympy | L3C | [
"L3C/MAX_DIVISOR"
] | 97dfc0 | nt_count_coprime_v1 | null | 6 | 0 | [
"L3C",
"MAX_DIVISOR"
] | 2 | 2.759 | 2026-02-08T17:20:00.043750Z | {
"verified": true,
"answer": 25624,
"timestamp": "2026-02-08T17:20:02.803005Z"
} | 91c1b0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 157,
"completion_tokens": 950
},
"timestamp": "2026-02-17T23:36:28.133Z",
"answer": 25624
},
{... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok_later"
},
{
"lemma": "MAX_PRIME_BELOW",
"st... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
372cfd | geo_count_lattice_rect_v1_798873815_142 | Compute the number of lattice points $(x, y)$ such that $0 \leq x \leq 121$ and $0 \leq y \leq 244$. | 29,890 | graphs = [
Graph(
let={
"a": Const(121),
"b": Const(244),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.001 | 2026-02-08T02:29:37.118685Z | {
"verified": true,
"answer": 29890,
"timestamp": "2026-02-08T02:29:37.119501Z"
} | faa4b4 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 259
},
"timestamp": "2026-02-08T19:03:49.625Z",
"answer": 29890
},
{
"i... | 1 | [] | {
"lo": -4.7,
"mid": -2.85,
"hi": -0.91
} | ||||
f38d4b | lin_form_endings_v1_1520064083_197 | Let $a = 70$, $b = 56$, $A = 21$, and $B = 45$. Let $g = \gcd(a, b)$. Define
$$
\text{numerator} = (a \cdot A + b \cdot B) - (a + b).
$$
Let $k = \left\lfloor \frac{\text{numerator}}{g} \right\rfloor + 1$. Let $s = 8802 \cdot k$, and let $M = 55976$. Compute the remainder when $s$ is divided by $M$. | 31,186 | graphs = [
Graph(
let={
"a_coeff": Const(70),
"b_coeff": Const(56),
"A_val": Const(21),
"B_val": Const(45),
"g_step": GCD(a=Ref("a_coeff"), b=Ref("b_coeff")),
"numerator": Sub(Sum(Mul(Ref("a_coeff"), Ref("A_val")), Mul(Ref("b_coeff"), R... | COMB | NT | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | lin_form_endings_v1 | null | 3 | null | [
"LIN_FORM"
] | 1 | 0.002 | 2026-02-08T03:07:46.659113Z | {
"verified": true,
"answer": 31186,
"timestamp": "2026-02-08T03:07:46.660880Z"
} | d713ce | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 243,
"completion_tokens": 887
},
"timestamp": "2026-02-10T13:00:08.457Z",
"answer": 31186
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.47,
"mid": 0.81,
"hi": 4.81
} | ||
eada26 | lte_diff_endings_v1_1520064083_1363 | Let $a = 9$, $b = 5$, $p = 2$, $K = 3$, and $N = 175104$. Define $\text{diff} = a - b$. Let $v_p(\text{diff})$ be the largest integer $k$ such that $p^k$ divides $\text{diff}$. Define $m = K - v_p(\text{diff})$ and let $p^m$ be the $m$-th power of $p$. Compute the value of $\left\lfloor \frac{N}{p^m} \right\rfloor$. | 87,552 | graphs = [
Graph(
let={
"a_val": Const(9),
"b_val": Const(5),
"p_val": Const(2),
"K_val": Const(3),
"N_val": Const(175104),
"diff": Sub(Ref("a_val"), Ref("b_val")),
"vp_diff": MaxKDivides(target=Ref("diff"), base=Ref("p_val"... | NT | null | COMPUTE | sympy | LTE_DIFF | [
"LTE_DIFF"
] | cf8260 | lte_diff_endings_v1 | null | 3 | null | [
"LTE_DIFF"
] | 1 | 0.001 | 2026-02-08T03:56:43.791115Z | {
"verified": true,
"answer": 87552,
"timestamp": "2026-02-08T03:56:43.792110Z"
} | 50ad36 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 227,
"completion_tokens": 220
},
"timestamp": "2026-02-18T06:56:17.877Z",
"answer": 87552
}
] | 2 | [
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
2ce766 | nt_sum_over_divisible_v1_1820931509_692 | Let $A$ be the set of ordered pairs $(x, y)$ of positive integers such that $xy = 6241$. Define $d$ to be the minimum value of $x + y$ over all pairs $(x, y) \in A$. Let $S$ be the set of positive integers $n$ such that $1 \leq n \leq 16384$ and $n$ is divisible by $d$. Define $r$ to be the sum of all elements in $S$. ... | 5,682 | graphs = [
Graph(
let={
"_n": Const(77440),
"upper": Const(16384),
"divisor": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const... | NT | null | SUM | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"B3"
] | 9464f4 | nt_sum_over_divisible_v1 | negation_mod | 5 | 0 | [
"B3",
"COUNT_CARTESIAN"
] | 2 | 5.53 | 2026-02-08T11:49:29.574101Z | {
"verified": true,
"answer": 5682,
"timestamp": "2026-02-08T11:49:35.104484Z"
} | b5c0be | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 1116
},
"timestamp": "2026-02-14T19:30:00.200Z",
"answer": 5682
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma":... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
aba5f5 | comb_catalan_compute_v1_1431428450_743 | Let $n = 11$. The $n$-th Catalan number is defined as $C_n = \frac{1}{n+1} \binom{2n}{n}$. Let $c$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 1110$. Compute the remainder when $c - C_n$ is divided by $71720$. | 13,489 | graphs = [
Graph(
let={
"n": Const(11),
"result": Catalan(Ref("n")),
"_c": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name... | COMB | null | COMPUTE | sympy | COMB1 | [
"COMB1"
] | 9f12f1 | comb_catalan_compute_v1 | negation_mod | 3 | 0 | [
"COMB1"
] | 1 | 0.003 | 2026-02-08T13:39:34.086543Z | {
"verified": true,
"answer": 13489,
"timestamp": "2026-02-08T13:39:34.089846Z"
} | 2d2a24 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 207,
"completion_tokens": 1323
},
"timestamp": "2026-02-24T18:47:57.664Z",
"answer": 13489
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
011349 | modular_sum_quadratic_residues_v1_865884756_6466 | Let $p$ be the smallest divisor of 82307671 that is at least 2. Compute $\frac{p(p-1)}{4}$. | 46,764 | graphs = [
Graph(
let={
"_n": Const(2),
"p": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Ref("_n")), Divides(divisor=Var("d"), dividend=Const(82307671))))),
"result": Div(Mul(Ref("p"), Sub(Ref("p"), Const(1))), Const(4)),
},
goal=... | NT | null | SUM | sympy | MAX_PRIME_BELOW | [
"MIN_PRIME_FACTOR"
] | bc3776 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 0.004 | 2026-02-08T19:13:26.652363Z | {
"verified": true,
"answer": 46764,
"timestamp": "2026-02-08T19:13:26.655999Z"
} | db1bc2 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 3156
},
"timestamp": "2026-02-18T21:37:38.717Z",
"answer": 46764
},
{... | 1 | [
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
bfe0b7 | algebra_poly_eval_v1_898971024_419 | Let $x = 29$. Compute the value of
$$
\left| x^{\sum_{k=1}^{2} \phi(k) \left\lfloor \frac{2}{k} \right\rfloor} - 3x^2 + 2x - 2 \right|.
$$ | 21,922 | graphs = [
Graph(
let={
"_n": Const(2),
"x": Const(29),
"result": Sum(Pow(Ref("x"), Summation(var="k", start=Const(1), end=Const(2), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(2), Var("k")))))), Mul(Const(-3), Pow(Ref("x"), Const(2))), Mul(Ref("_n"), Ref("x")), Const(... | NT | null | COMPUTE | sympy | K2 | [
"K2"
] | 6897ab | algebra_poly_eval_v1 | null | 4 | 0 | [
"K2"
] | 1 | 0.002 | 2026-02-08T15:27:01.111672Z | {
"verified": true,
"answer": 21922,
"timestamp": "2026-02-08T15:27:01.113266Z"
} | a6aca5 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 110,
"completion_tokens": 684
},
"timestamp": "2026-02-16T06:07:22.931Z",
"answer": 21922
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
c56e2b | comb_count_surjections_v1_1978505735_83 | Let $S_2$ be the set of all ordered pairs of positive odd integers $(x_{11}, x_{21})$ such that $x_{11} + x_{21} = 14$. Let $s = |S_2|$. Let $S_3$ be the set of all ordered triples of positive odd integers $(x_1, x_2, x_3)$ such that $x_1 + x_2 + x_3 = s$. Let $n = |S_3|$. Compute the remainder when $48031 \cdot 2! \cd... | 25,418 | graphs = [
Graph(
let={
"_n": Const(82014),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2"), Var("x3")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsPositive(arg=Var(name='x3')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var... | COMB | null | COUNT | sympy | COMB1 | [
"COMB1/COMB1"
] | b2c526 | comb_count_surjections_v1 | null | 7 | 0 | [
"COMB1"
] | 1 | 0.005 | 2026-02-08T15:11:08.774540Z | {
"verified": true,
"answer": 25418,
"timestamp": "2026-02-08T15:11:08.779821Z"
} | 53e20b | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 267,
"completion_tokens": 1220
},
"timestamp": "2026-02-24T19:58:18.137Z",
"answer": 25418
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -2.43,
"mid": 1.2,
"hi": 4.84
} | ||
3e4f55 | algebra_quadratic_discriminant_v1_2051736721_3251 | Let $a = -1$ and $b = 9$. Define $c = \sum_{k=1}^{4} \phi(k) \left\lfloor \frac{4}{k} \right\rfloor$, where $\phi$ denotes Euler's totient function. Let $T$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 2700$, $\gcd(p, q) = 1$, and $p < q$. Compute $b^2 - |T| \cdo... | 121 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(-1),
"b": Const(9),
"c": Summation(var="k", start=Const(1), end=Const(4), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Ref("_n"), Var("k"))))),
"result": Sub(Pow(Ref("b"), Const(2)), Mul(CountOverSet(s... | NT | null | COMPUTE | sympy | K2 | [
"COPRIME_PAIRS",
"K2"
] | 5d07bf | algebra_quadratic_discriminant_v1 | null | 4 | 0 | [
"COPRIME_PAIRS",
"K2"
] | 2 | 0.023 | 2026-02-08T17:12:35.596972Z | {
"verified": true,
"answer": 121,
"timestamp": "2026-02-08T17:12:35.620027Z"
} | fb25b4 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 169,
"completion_tokens": 1707
},
"timestamp": "2026-02-17T22:22:01.178Z",
"answer": 121
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status":... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dc2419 | antilemma_sum_primes_v1_1520064083_2091 | Let $m = 2$ and $n = 3$. Define $s$ to be the sum of all prime numbers $p$ such that $m \leq p \leq n$. Let $A = s \bmod 307$ and let $B$ be the largest prime number at most $2006$. Let $C = s \bmod 317$. Compute $A + B \cdot C$. | 10,020 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(3),
"x": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_m")), Leq(Var("n"), Ref("_n")), IsPrime(Var("n"))))),
"Q": Sum(Mod(value=Ref("x"), modulus=Const(307)), Mul(MaxOverSet(set=... | NT | null | COMPUTE | sympy | MAX_PRIME_BELOW | [
"MAX_PRIME_BELOW",
"SUM_PRIMES"
] | c54bfc | antilemma_sum_primes_v1 | two_moduli | 3 | 0 | [
"MAX_PRIME_BELOW",
"SUM_PRIMES"
] | 2 | 0.001 | 2026-02-08T04:30:44.501225Z | {
"verified": true,
"answer": 10020,
"timestamp": "2026-02-08T04:30:44.502634Z"
} | 1efeed | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 185,
"completion_tokens": 250
},
"timestamp": "2026-02-18T11:51:15.378Z",
"answer": 10020
}
] | 2 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "SUM_PRIMES",
"status... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
2f0029 | geo_count_lattice_triangle_v1_1218484723_2217 | Let $M = |196 \cdot 200 + 233 \cdot (-90)|$ and $R = \gcd(196, 90) + \gcd(|233 - 196|, |200 - 90|) + \gcd(233, 200)$. Compute $\frac{M + 2 - R}{2}$. | 9,114 | graphs = [
Graph(
let={
"_n": Const(200),
"area_2x": Abs(arg=Sum(Mul(Const(value=196), Const(value=200)), Mul(Const(value=233), Sub(left=Const(value=0), right=Const(value=90))))),
"boundary": Sum(GCD(a=Abs(arg=Const(value=196)), b=Abs(arg=Const(value=90))), GCD(a=Abs(arg=... | GEOM | NT | COUNT | sympy | QF_PSD_DISTINCT | [
"QF_PSD_DISTINCT"
] | a8f9cb | geo_count_lattice_triangle_v1 | null | 3 | 0 | [
"QF_PSD_DISTINCT"
] | 1 | 0.006 | 2026-02-25T03:59:51.558322Z | {
"verified": true,
"answer": 9114,
"timestamp": "2026-02-25T03:59:51.564336Z"
} | 0398c0 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 187,
"completion_tokens": 647
},
"timestamp": "2026-03-29T03:35:44.369Z",
"answer": 9114
},
{
"id... | 1 | [
{
"lemma": "QF_PSD_DISTINCT",
"status": "ok"
}
] | {
"lo": -6.5,
"mid": -3.34,
"hi": -0.88
} | ||
ba53aa | comb_count_derangements_v1_1116507919_394 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 72$. Let $c = 4$ and let $m = |S|$. Let $k_{\text{sum}} = \sum_{k=1}^{c} k$. Define $n$ to be the largest prime number satisfying $m \leq n \leq k_{\text{sum}}$. Compute the numbe... | 1,854 | graphs = [
Graph(
let={
"_c": Const(4),
"_m": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=72)), Eq(left=GCD(a=Var(name='p'), b=Var(name='q... | NT | COMB | COUNT | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/SUM_ARITHMETIC/MAX_PRIME_BELOW"
] | d73388 | comb_count_derangements_v1 | null | 5 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW",
"SUM_ARITHMETIC"
] | 3 | 0.002 | 2026-02-08T02:33:22.729723Z | {
"verified": true,
"answer": 1854,
"timestamp": "2026-02-08T02:33:22.732008Z"
} | ae5081 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 238,
"completion_tokens": 1322
},
"timestamp": "2026-02-08T19:29:06.265Z",
"answer": 1854
},
{
"i... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{... | {
"lo": -7.22,
"mid": -5.02,
"hi": -3.03
} | ||
75c667 | sequence_count_fib_divisible_v1_677425708_3042 | Let $N = 65601$. Let $d$ be the number of nonnegative integers $j \leq N$ for which $\binom{N}{j}$ is odd. Let $r$ be the number of positive integers $n \leq 750$ such that $d$ divides the $n$-th Fibonacci number. Compute $r$. | 125 | graphs = [
Graph(
let={
"_n": Const(65601),
"upper": Const(750),
"d": CountOverSet(set=SolutionsSet(var=Var("j"), condition=And(Geq(Var("j"), Const(0)), Leq(Var("j"), Const(65601)), Eq(Mod(value=Binom(n=Ref("_n"), k=Var("j")), modulus=Const(2)), Const(1))), domain='nonneg... | NT | null | COUNT | sympy | V8 | [
"V8"
] | 86348e | sequence_count_fib_divisible_v1 | null | 7 | 0 | [
"V8"
] | 1 | 0.03 | 2026-02-08T05:27:07.469117Z | {
"verified": true,
"answer": 125,
"timestamp": "2026-02-08T05:27:07.499042Z"
} | 0ceb5e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 118,
"completion_tokens": 2049
},
"timestamp": "2026-02-12T08:52:13.250Z",
"answer": 125
},
{
... | 1 | [
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V8",
"status": "ok"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
b15321 | sequence_count_fib_divisible_v1_1520064083_5433 | Let $n$ range over the positive integers from $1$ to $1943$ inclusive. Define $\text{upper}$ to be the number of such $n$ for which $\gcd(n, 6) = 1$. Let $d = 3$. Define $\text{result}$ to be the number of positive integers $n$ with $1 \leq n \leq \text{upper}$ such that the $n$-th Fibonacci number is divisible by $d$.... | 162 | graphs = [
Graph(
let={
"_n": Const(6),
"upper": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(1943)), Eq(GCD(a=Var("n"), b=Ref("_n")), Const(1))))),
"d": Const(3),
"result": CountOverSet(set=SolutionsSe... | NT | null | COUNT | sympy | MAX_PRIME_BELOW | [
"C4"
] | 08d162 | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"C4",
"MAX_PRIME_BELOW"
] | 2 | 0.037 | 2026-02-08T06:47:24.939407Z | {
"verified": true,
"answer": 162,
"timestamp": "2026-02-08T06:47:24.976300Z"
} | e1bd53 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 152,
"completion_tokens": 1652
},
"timestamp": "2026-02-13T09:39:46.495Z",
"answer": 162
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
}
] | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
f02227 | antilemma_product_of_sums_v1_1742523217_3901 | Let $S_1$ be the sum of $i \cdot j$ over all ordered pairs $(i,j)$ with $1 \le i \le 6$ and $1 \le j \le 6$. Let $S_2$ be the sum of all integers $k$ from $\sum_{d\mid \gcd(4,9)} \mu(d)$ to $\min(x+y)$, where the minimum is taken over all ordered pairs $(x,y)$ of positive integers such that $x \cdot y = 81$. Let $x = S... | 82,244 | graphs = [
Graph(
let={
"_n": Const(95615),
"S1": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Const(1), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(6)), right=IntegerRange(start=Const(1), end=Const(6)))), expr... | NT | null | COMPUTE | sympy | B3 | [
"B3/SUM_ARITHMETIC",
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS"
] | 87798e | antilemma_product_of_sums_v1 | null | 6 | 0 | [
"B3",
"MOBIUS_COPRIME",
"PRODUCT_OF_SUMS",
"SUM_ARITHMETIC"
] | 4 | 3.728 | 2026-02-08T06:07:43.482644Z | {
"verified": true,
"answer": 82244,
"timestamp": "2026-02-08T06:07:47.210692Z"
} | 8f97c2 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 255,
"completion_tokens": 693
},
"timestamp": "2026-02-19T00:12:55.412Z",
"answer": 0
}
] | 0 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOBIUS_COPRIME",
"status": "ok"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "... | {
"lo": -6.48,
"mid": 1.54,
"hi": 9.56
} | ||
cff0af | nt_sum_phi_v1_1520064083_2002 | Let $U=529$. For each integer $n$ with $1\le n\le U$, let $\varphi(n)$ denote Euler's totient function, and define
$$R = \sum_{n=1}^{U} \varphi(n).$$
Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that
$$pq = 216, \qquad \gcd(p,q)=1, \qquad p<q.$$
Let $|S|$ be the nu... | 1 | graphs = [
Graph(
let={
"upper": Const(529),
"result": SumOverSet(set=MapOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")))), expr=EulerPhi(n=Var("n")))),
"Q": Bell(Mod(value=Abs(arg=Ref(name='result')), modulus=MaxO... | NT | COMB | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS/MAX_PRIME_BELOW"
] | ecca39 | nt_sum_phi_v1 | bell_mod | 8 | 0 | [
"COPRIME_PAIRS",
"MAX_PRIME_BELOW"
] | 2 | 0.031 | 2026-02-08T04:27:04.068455Z | {
"verified": true,
"answer": 1,
"timestamp": "2026-02-08T04:27:04.099028Z"
} | 4378cb | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 258,
"completion_tokens": 6310
},
"timestamp": "2026-02-12T00:38:34.244Z",
"answer": 1
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status... | {
"lo": 1.74,
"mid": 3.93,
"hi": 6.31
} | ||
85ee0f | comb_factorial_compute_v1_124444284_8166 | Let $m=6$. For each integer $n$ with $1\le n\le 960$, consider the condition that
\[n\equiv \left\lfloor \frac n2 \right\rfloor \pmod{5} \quad\text{and}\quad 6\mid F_n,
\]
where $F_n$ denotes the $n$th Fibonacci number. Let $N$ be the number of integers $n$ with $1\le n\le 960$ that satisfy this condition.
Consider al... | 40,320 | graphs = [
Graph(
let={
"_m": Const(6),
"_n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(960)), Congruent(a=Var(name='n'), b=Fl... | NT | null | COMPUTE | sympy | L3C | [
"L3C/COUNT_FIB_DIVISIBLE/B3"
] | e481c8 | comb_factorial_compute_v1 | null | 8 | 0 | [
"B3",
"COUNT_FIB_DIVISIBLE",
"L3C"
] | 3 | 0.002 | 2026-02-08T09:34:49.846230Z | {
"verified": true,
"answer": 40320,
"timestamp": "2026-02-08T09:34:49.848604Z"
} | b77c7d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1999
},
"timestamp": "2026-02-14T04:54:19.994Z",
"answer": 40320
},
... | 1 | [
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "ok_later"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3C",
"status": "ok"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6b8a06 | comb_sum_binomial_row_v1_784195855_6663 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Compute $n^{16}$. | 65,536 | graphs = [
Graph(
let={
"n": Const(16),
"result": Pow(CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=18)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | SUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.001 | 2026-02-08T08:46:38.527748Z | {
"verified": true,
"answer": 65536,
"timestamp": "2026-02-08T08:46:38.528509Z"
} | da4147 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 1246
},
"timestamp": "2026-02-13T21:50:23.677Z",
"answer": 65536
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"... | {
"lo": -5.55,
"mid": -3.01,
"hi": 0.32
} | ||
a59558 | nt_sum_divisors_mod_v1_1439011603_1546 | Let $n$ be the number of integers $t$ such that $18 \leq t \leq 3400$ and there exist integers $a$ and $b$ with $1 \leq a \leq 64$, $1 \leq b \leq 345$, and $t = 10a + 8b$. Let $\sigma$ be the sum of all positive divisors of $n$. Compute the remainder when $\sigma$ is divided by $11699$. | 5,952 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=64)), Geq(left=Var(name='b'), right=Const(value=... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_sum_divisors_mod_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T16:10:02.735361Z | {
"verified": true,
"answer": 5952,
"timestamp": "2026-02-08T16:10:02.740348Z"
} | 364d1b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 145,
"completion_tokens": 5221
},
"timestamp": "2026-02-16T22:06:58.170Z",
"answer": 5952
},
{... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
094ef0 | antilemma_k3_v1_865884756_285 | Compute
$$
\sum_{d \mid 11336} \phi(d),
$$
where $\phi$ denotes Euler's totient function. | 11,336 | graphs = [
Graph(
let={
"_n": Const(11336),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T15:17:58.147951Z | {
"verified": true,
"answer": 11336,
"timestamp": "2026-02-08T15:17:58.148369Z"
} | 2b874d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 141,
"completion_tokens": 420
},
"timestamp": "2026-02-10T06:32:08.732Z",
"answer": 11336
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
04397f | nt_count_coprime_v1_809748730_776 | Let $k$ be the largest prime number $n$ such that $2 \leq n \leq d$, where $d$ is the smallest prime divisor of $5676989$ that is at least $2$. Let $S$ be the set of all positive integers $n$ such that $1 \leq n \leq 59049$ and $\gcd(n, k) = 1$. Compute the number of elements in $S$. | 57,676 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": Const(59049),
"k": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Ref("_n")), Leq(Var("n"), MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(2)), Leq(Var("n"), MinOverSet(se... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW",
"MAX_PRIME_BELOW/MAX_PRIME_BELOW"
] | f15075 | nt_count_coprime_v1 | null | 4 | 0 | [
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 2 | 4.811 | 2026-02-08T11:44:59.727117Z | {
"verified": true,
"answer": 57676,
"timestamp": "2026-02-08T11:45:04.537677Z"
} | f9e057 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 139,
"completion_tokens": 1699
},
"timestamp": "2026-02-14T18:24:05.440Z",
"answer": 57676
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "L3b",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
2b88bb | nt_count_digit_sum_v1_1431428450_738 | Let $A$ be the number of positive integers $n$ such that $n \le 99999$ and the sum of the decimal digits of $n$ is 29. Let $B$ be the number of positive integers $n$ such that $1 \le n \le 145$ and $\gcd(n, 12) = 1$. Let $C = \sum_{k=1}^{15} k$. Compute the remainder when $A^2 + B \cdot A + C$ is divided by 67835. | 3,575 | graphs = [
Graph(
let={
"_m": Const(15),
"_n": Const(67835),
"upper": Const(99999),
"target_sum": Const(29),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(DigitSum(Var("... | NT | null | COUNT | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC",
"C4"
] | 742f34 | nt_count_digit_sum_v1 | quadratic_mod | 5 | 0 | [
"C4",
"SUM_ARITHMETIC"
] | 2 | 5.199 | 2026-02-08T13:39:06.051777Z | {
"verified": true,
"answer": 3575,
"timestamp": "2026-02-08T13:39:11.250763Z"
} | a0ce0f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 160,
"completion_tokens": 2128
},
"timestamp": "2026-02-15T19:05:05.988Z",
"answer": 3575
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
425c12 | nt_min_phi_inverse_v1_1978505735_2221 | Let $S$ be the set of all ordered pairs of positive integers $(x, y)$ such that $xy = 900$. Let $u$ be the minimum value of $x + y$ over all such pairs. Let $k = 18$. Consider the set of all positive integers $n$ such that $1 \leq n \leq u$ and $\phi(n) = k$, where $\phi$ denotes Euler's totient function. Let $r$ be th... | 60,247 | graphs = [
Graph(
let={
"_n": Const(900),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y"))))... | NT | null | EXTREMUM | sympy | B3 | [
"B3"
] | 0cd20d | nt_min_phi_inverse_v1 | null | 7 | 0 | [
"B3"
] | 1 | 0.013 | 2026-02-08T16:46:59.845635Z | {
"verified": true,
"answer": 60247,
"timestamp": "2026-02-08T16:46:59.858747Z"
} | f04118 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 168,
"completion_tokens": 2567
},
"timestamp": "2026-02-17T11:20:29.709Z",
"answer": 60247
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
dbf407 | modular_sum_quadratic_residues_v1_153355830_2587 | Let $m = 4$ and $n = \sum_{k=1}^{33} k$. Let $p$ be the number of positive integers $k$ such that $1 \leq k \leq n$ and $\gcd(k, 14) = 1$. Compute $\frac{p(p-1)}{m}$. | 14,460 | graphs = [
Graph(
let={
"_m": Const(4),
"_n": Summation(var="k", start=Const(1), end=Const(33), expr=Var("k")),
"p": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(14)), Const(1))))),... | NT | null | SUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC/C4"
] | fd2dd8 | modular_sum_quadratic_residues_v1 | null | 3 | 0 | [
"C4",
"SUM_ARITHMETIC"
] | 2 | 0.002 | 2026-02-08T07:14:11.769040Z | {
"verified": true,
"answer": 14460,
"timestamp": "2026-02-08T07:14:11.771486Z"
} | 616f68 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 130,
"completion_tokens": 420
},
"timestamp": "2026-02-15T18:54:50.572Z",
"answer": 14460
},
{
"id": 11,
... | 2 | [
{
"lemma": "C4",
"status": "ok_later"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "SUM_ARITHM... | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.73
} | ||
7fcf9f | algebra_quadratic_discriminant_v1_677425708_1899 | Let $m$ be the smallest positive integer such that $2^3$ divides $m!$. Let $p$ be the maximum value of $xy$ over all ordered pairs $(x, y)$ of positive integers such that $x + y = m$. Let $D = b^2 - 4ac$, where $a = 1$, $b = -8$, and $c = 16$. Define $\delta = 2$ if $D > 0$, $\delta = 1$ if $D = 0$, and $\delta = 0$ ot... | 37,635 | graphs = [
Graph(
let={
"_m": Const(2),
"_n": Const(37636),
"a": Const(1),
"b": Const(-8),
"c": Const(16),
"D": Sub(Pow(Ref("b"), Const(2)), Mul(MaxOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condit... | NT | null | COMPUTE | sympy | V5 | [
"V5/B1"
] | 1d4cb9 | algebra_quadratic_discriminant_v1 | null | 7 | 0 | [
"B1",
"V5"
] | 2 | 0.005 | 2026-02-08T04:37:55.045626Z | {
"verified": true,
"answer": 37635,
"timestamp": "2026-02-08T04:37:55.050186Z"
} | 0897cc | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 240,
"completion_tokens": 430
},
"timestamp": "2026-02-10T02:45:28.344Z",
"answer": 37635
},
{
"i... | 2 | [
{
"lemma": "B1",
"status": "ok_later"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V5",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemm... | {
"lo": -10,
"mid": -6.47,
"hi": -2.95
} | ||
0485fa | comb_catalan_compute_v1_124444284_3055 | Let $n$ be the number of ordered pairs $(i, j)$ of positive integers such that $1 \leq i \leq 10$, $1 \leq j \leq 11$, and $i + j = 11$. Define $r = C_n$, where $C_n$ denotes the $n$-th Catalan number. Compute the value of $65536 - r$. | 48,740 | graphs = [
Graph(
let={
"_n": Const(11),
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Ref("_n")), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(10)), right=IntegerRange(start=Const(1), end=Con... | COMB | null | COMPUTE | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_catalan_compute_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.013 | 2026-02-08T05:10:26.547857Z | {
"verified": true,
"answer": 48740,
"timestamp": "2026-02-08T05:10:26.561312Z"
} | a54098 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 196,
"completion_tokens": 723
},
"timestamp": "2026-02-24T02:57:14.706Z",
"answer": 48740
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -5.98,
"mid": -3.97,
"hi": -1.94
} | ||
76a6f8 | sequence_lucas_compute_v1_1439011603_2591 | Let $n$ be the minimum value of $x + y$ over all ordered pairs $(x, y)$ of positive integers such that $xy = 100$. Let $L_n$ denote the $n$th Lucas number, defined by $L_1 = 1$, $L_2 = 3$, and $L_k = L_{k-1} + L_{k-2}$ for $k \geq 3$. Compute the remainder when $44649 \cdot L_n$ is divided by $97019$. | 56,164 | graphs = [
Graph(
let={
"_n": Const(100),
"n": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Ref("_n")))), expr=Sum(Var("x"), Var("y")))),
... | NT | null | COMPUTE | sympy | B3 | [
"B3"
] | 0cd20d | sequence_lucas_compute_v1 | null | 5 | 0 | [
"B3"
] | 1 | 0.001 | 2026-02-08T16:52:34.167853Z | {
"verified": true,
"answer": 56164,
"timestamp": "2026-02-08T16:52:34.168989Z"
} | d8d7d7 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1176
},
"timestamp": "2026-02-17T14:16:26.413Z",
"answer": 56164
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
317691 | diophantine_product_count_v1_397696148_1667 | Let $k = 840$ and $\text{upper} = 313$. Let $r$ be the number of positive integers $x$ such that $1 \le x \le \text{upper}$, $x$ divides $k$, and $k/x \le \text{upper}$. Compute the value of
$$
r + 2^{r \bmod 14} \bmod 75964.
$$ | 29 | graphs = [
Graph(
let={
"k": Const(840),
"upper": Const(313),
"result": CountOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Divides(divisor=Var("x"), dividend=Ref("k")), Leq(Div(Ref("k"), Var("x")), Ref("upper"))... | NT | null | COUNT | sympy | C4 | [
"C4/OMEGA_ONE",
"BIG_OMEGA_ZERO"
] | 12c89c | diophantine_product_count_v1 | null | 4 | 0 | [
"BIG_OMEGA_ZERO",
"C4",
"OMEGA_ONE"
] | 3 | 0.145 | 2026-02-08T12:42:30.841078Z | {
"verified": true,
"answer": 29,
"timestamp": "2026-02-08T12:42:30.986489Z"
} | da4157 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 1480
},
"timestamp": "2026-02-15T04:03:36.305Z",
"answer": 29
},
{
... | 1 | [
{
"lemma": "BIG_OMEGA_ZERO",
"status": "ok"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "OMEGA_ONE",
"status": "ok_later"... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
6edd7b | antilemma_cartesian_v1_1742523217_2043 | Let $S$ be the set of all ordered pairs $(a,b)$ such that $a$ is an integer with $1 \le a \le 27$ and $b$ is an integer with $1 \le b \le 28$. Compute the number of elements in $S$. | 756 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(27)), right=IntegerRange(start=Const(1), end=Const(28)))),
},
goal=Ref("x"),
)
] | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0 | 2026-02-08T04:25:51.197061Z | {
"verified": true,
"answer": 756,
"timestamp": "2026-02-08T04:25:51.197341Z"
} | 461c0d | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 171,
"completion_tokens": 134
},
"timestamp": "2026-02-24T00:40:51.709Z",
"answer": 756
},
{
"id"... | 2 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
},
{
"lemma": "V8_SUM",
"status"... | {
"lo": -10,
"mid": -7.79,
"hi": -5.57
} | ||
a15436 | diophantine_product_count_v1_1439011603_50 | Let $k$ be the number of ordered pairs $(a, b)$ of positive integers such that $1 \leq a \leq 35$ and $1 \leq b \leq 36$.
Let $u$ be the sum of all positive integers $n$ such that $1 \leq n \leq 324$ and $n$ is divisible by $162$.
Let $r$ be the number of positive integers $x$ such that $1 \leq x \leq u$, $x$ divides... | 55,341 | graphs = [
Graph(
let={
"_n": Const(60634),
"k": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(35)), right=IntegerRange(start=Const(1), end=Const(36)))),
"upper": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1... | NT | COMB | COUNT | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN",
"SUM_DIVISIBLE"
] | 7d6259 | diophantine_product_count_v1 | null | 6 | 0 | [
"COUNT_CARTESIAN",
"SUM_DIVISIBLE"
] | 2 | 0.03 | 2026-02-08T15:08:26.668720Z | {
"verified": true,
"answer": 55341,
"timestamp": "2026-02-08T15:08:26.699112Z"
} | dfd3f3 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 190,
"completion_tokens": 1445
},
"timestamp": "2026-02-16T01:15:30.018Z",
"answer": 55341
},
... | 1 | [
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONS... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
7ec275 | sequence_count_fib_divisible_v1_1440796553_1316 | Let $n$ be a positive integer. Define $\phi(k)$ to be Euler's totient function. Let
$$
S = \sum_{k=1}^{33} \phi(k) \left\lfloor \frac{33}{k} \right\rfloor.
$$
Determine the number of positive integers $n$ such that $1 \leq n \leq S$ and $5$ divides the $n$th Fibonacci number.
Compute this number. | 112 | graphs = [
Graph(
let={
"_n": Const(33),
"upper": Summation(var="k", start=Const(1), end=Ref("_n"), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(Const(33), Var("k"))))),
"d": Const(5),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"K2"
] | 6897ab | sequence_count_fib_divisible_v1 | null | 6 | 0 | [
"K2",
"MIN_PRIME_FACTOR"
] | 2 | 0.193 | 2026-02-08T13:38:34.147195Z | {
"verified": true,
"answer": 112,
"timestamp": "2026-02-08T13:38:34.340046Z"
} | b73b53 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 981
},
"timestamp": "2026-02-15T19:27:00.186Z",
"answer": 112
},
{
... | 1 | [
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok"
},
{
"lemma": "LTE_SUM",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
d85710 | nt_count_primes_v1_784195855_5653 | Let $P$ be the set of all ordered pairs $(x, y)$ of positive integers such that $x \cdot y = 25000000$. Let $s$ be the minimum value of $x + y$ over all such pairs. Let $r$ be the number of prime numbers $n$ such that $2 \leq n \leq s$. Compute $r + \phi(r + 1) + \tau(r + 1)$, where $\phi(n)$ denotes the number of posi... | 1,565 | graphs = [
Graph(
let={
"_n": Const(2),
"upper": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(25000000)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_primes_v1 | null | 6 | 0 | [
"B3"
] | 1 | 0.233 | 2026-02-08T08:01:45.444146Z | {
"verified": true,
"answer": 1565,
"timestamp": "2026-02-08T08:01:45.677389Z"
} | 63b75d | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 183,
"completion_tokens": 1982
},
"timestamp": "2026-02-13T14:10:30.247Z",
"answer": 1565
},
{... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -3.51,
"mid": 1.33,
"hi": 6.56
} | ||
96274c | comb_count_surjections_v1_677425708_389 | Let $n$ be the number of ordered pairs $(i, j)$ of integers such that $1 \leq i \leq 7$, $1 \leq j \leq 7$, and $i + j = 8$. Let $k = 4$. Compute $k! \cdot S(n, k)$, where $S(n, k)$ denotes the Stirling number of the second kind. | 8,400 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("i"), Var("j")]), condition=Eq(Sum(Var("i"), Var("j")), Const(8)), domain=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(7)), right=IntegerRange(start=Const(1), end=Const(7))))),
"k": Con... | COMB | null | COUNT | sympy | COUNT_SUM_EQUALS | [
"COUNT_SUM_EQUALS"
] | 75ab0f | comb_count_surjections_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS"
] | 1 | 0.01 | 2026-02-08T03:16:19.954454Z | {
"verified": true,
"answer": 8400,
"timestamp": "2026-02-08T03:16:19.964755Z"
} | da9211 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 203,
"completion_tokens": 1393
},
"timestamp": "2026-02-08T20:30:53.966Z",
"answer": 8400
},
{
"i... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V8_SU... | {
"lo": -3.83,
"mid": -1.68,
"hi": 1.09
} | ||
c9d1a2 | antilemma_k3_v1_898971024_476 | Let $n = 50186$. Compute the sum of $\phi(d)$ over all positive divisors $d$ of $n$, where $\phi$ denotes Euler's totient function. | 50,186 | graphs = [
Graph(
let={
"_n": Const(50186),
"x": SumOverDivisors(n=Ref(name='_n'), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 3 | 0 | [
"K3"
] | 1 | 0.001 | 2026-02-08T15:27:59.711730Z | {
"verified": true,
"answer": 50186,
"timestamp": "2026-02-08T15:27:59.712318Z"
} | fbe7e4 | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 1,
"correct": {
"strict": false,
"boxed": false,
"relaxed": true
},
"usage": {
"prompt_tokens": 100,
"completion_tokens": 227
},
"timestamp": "2026-02-16T06:05:14.148Z",
"answer": 50184
},
{
"id": 11,... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"st... | {
"lo": -8.26,
"mid": -5.01,
"hi": -1.76
} | ||
469add | diophantine_sum_product_min_v1_971394319_1999 | Let $S = 74$ and $P = 528$. Consider the set of all integers $x$ such that $1 \leq x \leq 73$ and $x(S - x) = P$. Let $m$ be the smallest such integer $x$. Compute $m$. | 8 | graphs = [
Graph(
let={
"S": Const(74),
"P": Const(528),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Const(73)), Eq(Mul(Var("x"), Sub(Ref("S"), Var("x"))), Ref("P"))))),
},
goal=Ref("result"),
... | NT | null | EXTREMUM | sympy | SUM_ARITHMETIC | [
"SUM_ARITHMETIC"
] | eb34f0 | diophantine_sum_product_min_v1 | null | 3 | 0 | [
"SUM_ARITHMETIC"
] | 1 | 0.033 | 2026-02-08T14:04:48.091414Z | {
"verified": true,
"answer": 8,
"timestamp": "2026-02-08T14:04:48.124805Z"
} | f1757e | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 483
},
"timestamp": "2026-02-15T23:40:34.688Z",
"answer": 8
},
{
... | 1 | [
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "SUM_ARITHMETIC",
"status": "ok"
},
{
"lemma": "V8",
"status": "n... | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
47c6be | sequence_fibonacci_compute_v1_1742523217_4112 | Let $n$ be the number of positive integers at most $73$ that are relatively prime to $6$. Define $\mathcal{R} = F_n$, the $n$-th Fibonacci number. Compute the value of $\mathcal{R}$. Determine the value of $Q$, which is $\mathcal{R}$. | 75,025 | graphs = [
Graph(
let={
"_n": Const(73),
"n": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("_n")), Eq(GCD(a=Var("n"), b=Const(6)), Const(1))))),
"result": Fibonacci(arg=Ref(name='n')),
"Q": Ref("result"),... | NT | null | COMPUTE | sympy | C4 | [
"C4"
] | 08d162 | sequence_fibonacci_compute_v1 | null | 3 | 0 | [
"C4"
] | 1 | 0.001 | 2026-02-08T06:59:56.410012Z | {
"verified": true,
"answer": 75025,
"timestamp": "2026-02-08T06:59:56.411362Z"
} | 4b5891 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 108,
"completion_tokens": 925
},
"timestamp": "2026-02-13T06:51:21.673Z",
"answer": 75025
},
{... | 1 | [
{
"lemma": "C4",
"status": "ok"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
7952f7 | antilemma_sum_equals_v1_865884756_1092 | Let $ n $ be the number of integers $ t $ such that $ 16 \leq t \leq 162 $ and there exist positive integers $ a $, $ b $ with $ 1 \leq a \leq 3 $, $ 1 \leq b \leq 22 $, and $ t = 10a + 6b $. Let $ x $ be the number of ordered pairs $ (i, j) $ of positive integers such that $ 1 \leq i \leq 65 $, $ 1 \leq j \leq 66 $, a... | 68 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=3)), Geq(left=Var(name='b'), right=Const(value=... | COMB | GEOM | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | ada383 | antilemma_sum_equals_v1 | null | 5 | 0 | [
"COUNT_SUM_EQUALS",
"LIN_FORM"
] | 2 | 0.174 | 2026-02-08T15:47:16.577360Z | {
"verified": true,
"answer": 68,
"timestamp": "2026-02-08T15:47:16.751247Z"
} | 9dcd43 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 272,
"completion_tokens": 4965
},
"timestamp": "2026-02-24T18:36:27.463Z",
"answer": 68
},
{
"id... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8",
"st... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
df9c7c | modular_count_residue_v1_458359167_691 | Let $ u = 58081 $ and $ m = 29 $. Define $ r $ to be the sum of all positive integers $ n $ such that $ 1 \leq n \leq 26 $ and $ n $ is divisible by $ 26 $. Let $ S $ be the set of all positive integers $ n $ such that $ 1 \leq n \leq u $ and $ n \equiv r \pmod{m} $. Compute the number of elements in $ S $. | 2,002 | graphs = [
Graph(
let={
"_n": Const(26),
"upper": Const(58081),
"m": Const(29),
"r": SumOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Const(26)), Eq(Mod(value=Var("n"), modulus=Ref("_n")), Const(0))))),
... | NT | null | COUNT | sympy | SUM_DIVISIBLE | [
"SUM_DIVISIBLE"
] | 02dbe3 | modular_count_residue_v1 | null | 4 | 0 | [
"SUM_DIVISIBLE"
] | 1 | 2.695 | 2026-02-08T03:30:26.584245Z | {
"verified": true,
"answer": 2002,
"timestamp": "2026-02-08T03:30:29.279089Z"
} | a1cd61 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 218,
"completion_tokens": 852
},
"timestamp": "2026-02-10T14:41:03.166Z",
"answer": 2002
},
{
"id... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "SUM_DIVISIBLE",
"status": "ok"
}
] | {
"lo": -9.14,
"mid": -6.05,
"hi": -3.74
} | ||
bcf0fd | antilemma_k3_v1_397696148_2307 | Compute the sum of $\phi(d)$ over all positive divisors $d$ of $89604$, where $\phi$ denotes Euler's totient function. | 89,604 | graphs = [
Graph(
let={
"x": SumOverDivisors(n=Const(value=89604), var='d', expr=EulerPhi(n=Var(name='d'))),
},
goal=Ref("x"),
)
] | NT | COMB | COMPUTE | sympy | K3 | [
"K3"
] | 54c41e | antilemma_k3_v1 | null | 4 | 0 | [
"K3"
] | 1 | 0 | 2026-02-08T13:06:09.022322Z | {
"verified": true,
"answer": 89604,
"timestamp": "2026-02-08T13:06:09.022768Z"
} | cac7a0 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 77,
"completion_tokens": 6930
},
"timestamp": "2026-02-15T09:21:47.504Z",
"answer": 89604
},
{... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "K3",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
3ad839 | alg_poly4_min_v1_1218484723_1390 | Let $C = \left|\{ (a_1, b_1) : 1 \leq a_1, b_1 \leq 35,\ 20b_1^2 - 12a_1b_1 + 41a_1^2 \leq 12544 \}\right|$. Find the minimum value $Q$ of the expression $$1466748a^4 - 7822656a^3b + 15645312a^2b^2 - 13906944ab^3 + 4653756b^4$$ over all positive integers $a, b$ with $1 \leq a \leq 377$ and $1 \leq b \leq C$. | 36,216 | graphs = [
Graph(
let={
"_n": Const(2),
"result": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("a"), Var("b")]), condition=And(Geq(Var("a"), Const(1)), Leq(Var("a"), Const(377)), Geq(Var("b"), Const(1)), Leq(Var("b"), CountOverSet(set=SolutionsSet(var=Tuple(elem... | ALG | null | COMPUTE | sympy | QF_PSD_COUNT_LEQ | [
"QF_PSD_COUNT_LEQ"
] | 009d0f | alg_poly4_min_v1 | null | 6 | 0 | [
"QF_PSD_COUNT_LEQ"
] | 1 | 0.354 | 2026-02-25T03:07:45.202423Z | {
"verified": true,
"answer": 36216,
"timestamp": "2026-02-25T03:07:45.556511Z"
} | 68ef74 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 269,
"completion_tokens": 16732
},
"timestamp": "2026-03-10T06:47:51.762Z",
"answer": 36216
},
{
... | 1 | [
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "QF_PSD_COUNT_LEQ",
"status": "ok"
}
] | {
"lo": -2.47,
"mid": 1.2,
"hi": 4.81
} | ||
898fe3 | nt_count_gcd_equals_v1_677425708_4129 | Let $N = 15625$. Consider the set of all ordered pairs $(x,y)$ of positive integers such that $xy = N$. Let $s$ be the sum $x + y$ for each such pair. Define $k$ to be the minimum value of $s$ over all such pairs.
Now, let $U = 27225$. Determine the number of positive integers $n$ such that $1 \leq n \leq U$ and $\gcd... | 108 | graphs = [
Graph(
let={
"upper": Const(27225),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(15625)))), expr=Sum(Var("x"), Var("y"... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B3"
] | 1 | 2.388 | 2026-02-08T06:26:27.151406Z | {
"verified": true,
"answer": 108,
"timestamp": "2026-02-08T06:26:29.539594Z"
} | ecddea | CC BY 4.0 | [
{
"id": 8,
"model": "mathstral",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 178,
"completion_tokens": 346
},
"timestamp": "2026-02-15T17:28:57.440Z",
"answer": 181
},
{
"id": 11,
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "LTE_DIFF",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
}
] | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
2f10ed | comb_count_partitions_v1_168721529_841 | Let $T$ be the set of all integers $t$ with $20 \leq t \leq 120$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 13$, $1 \leq b \leq 3$, and $t = 6a + 14b$. Let $n$ be the number of elements in $T$. Let $P$ be the number of integer partitions of $n$. Compute $50625 - P$. | 19,440 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=13)), Geq(left=Var(name='b'), right=Const(value=... | COMB | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | comb_count_partitions_v1 | null | 6 | 0 | [
"LIN_FORM"
] | 1 | 0.001 | 2026-02-08T13:19:09.684935Z | {
"verified": true,
"answer": 19440,
"timestamp": "2026-02-08T13:19:09.686234Z"
} | 8e7d45 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 225,
"completion_tokens": 2511
},
"timestamp": "2026-02-09T09:48:29.355Z",
"answer": 19440
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "V8",
"st... | {
"lo": 1.36,
"mid": 4.2,
"hi": 6.62
} | ||
9ef478 | nt_count_intersection_v1_238844314_620 | Let $N = 50000$ and $a = 7$. Define
$$
b = \sum_{k=1}^{5} \phi(k) \left\lfloor \frac{\max\{ n \mid 2 \leq n \leq d_{\min},\ n \text{ is prime} \}}{k} \right\rfloor,
$$
where $d_{\min}$ is the smallest divisor of 2695 that is at least 2. Let $r$ be the number of positive integers $n \leq N$ such that $a$ divides $n$ and... | 59,020 | graphs = [
Graph(
let={
"_m": Const(66949),
"_n": Const(44121),
"N": Const(50000),
"a": Const(7),
"b": Summation(var="k", start=Const(1), end=Const(5), expr=Mul(EulerPhi(n=Var("k")), Floor(Div(MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR/MAX_PRIME_BELOW/K2"
] | ff4923 | nt_count_intersection_v1 | null | 7 | 0 | [
"K2",
"MAX_PRIME_BELOW",
"MIN_PRIME_FACTOR"
] | 3 | 5.231 | 2026-02-08T13:26:00.586648Z | {
"verified": true,
"answer": 59020,
"timestamp": "2026-02-08T13:26:05.817340Z"
} | fd337f | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 195,
"completion_tokens": 2259
},
"timestamp": "2026-02-15T15:22:45.834Z",
"answer": 59020
},
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K2",
"status": "ok_later"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "ok_later"
},
{
"lemma": "MAX_VAL",
"status": "no"... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
18e2b6 | nt_max_prime_below_v1_1520064083_2582 | Let $S$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 18$, $\gcd(p, q) = 1$, and $p < q$. Let $m$ be the number of elements in $S$. Let $T$ be the set of all prime numbers $n$ such that $n \geq m$ and $n \leq 35344$. Compute the largest element in $T$. | 35,339 | graphs = [
Graph(
let={
"upper": Const(35344),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 4 | 0 | [
"COPRIME_PAIRS"
] | 1 | 3.931 | 2026-02-08T04:52:10.072989Z | {
"verified": true,
"answer": 35339,
"timestamp": "2026-02-08T04:52:14.003750Z"
} | 5f8e3e | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 213,
"completion_tokens": 3426
},
"timestamp": "2026-02-11T22:23:56.076Z",
"answer": 35339
},
{
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"sta... | {
"lo": -3.42,
"mid": 1.86,
"hi": 7.55
} | ||
5eb274 | geo_count_lattice_rect_v1_48377204_697 | Compute the number of lattice points in the rectangle $[0, 44] \times [0, 61]$. | 2,790 | graphs = [
Graph(
let={
"a": Const(44),
"b": Const(61),
"result": LatticePointsRect(a=Ref(name='a'), b=Ref(name='b')),
},
goal=Ref("result"),
)
] | GEOM | null | COUNT | sympy | [] | geo_count_lattice_rect_v1 | null | 3 | 0 | null | null | 0.002 | 2026-02-08T15:39:12.991923Z | {
"verified": true,
"answer": 2790,
"timestamp": "2026-02-08T15:39:12.993598Z"
} | 3ca582 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 135,
"completion_tokens": 228
},
"timestamp": "2026-02-24T18:15:05.917Z",
"answer": 2790
},
{
"i... | 2 | [] | {
"lo": -10,
"mid": -7.42,
"hi": -4.85
} | ||||
a21a80 | antilemma_sum_equals_v1_1915831931_750 | Let $n$ be the number of ordered pairs $(x_1, x_2)$ of positive odd integers such that $x_1 + x_2 = 204$. Let $x$ be the number of ordered pairs $(i, j)$ of positive integers with $1 \leq i \leq 100$ and $1 \leq j \leq 100$ such that $i + j = n$. Compute the remainder when $99667x$ is divided by $61219$. | 10,774 | graphs = [
Graph(
let={
"_n": CountOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x1"), Var("x2")]), condition=And(IsPositive(arg=Var(name='x1')), IsPositive(arg=Var(name='x2')), IsOdd(arg=Var(name='x1')), IsOdd(arg=Var(name='x2')), Eq(Sum(Var("x1"), Var("x2")), Const(204))))),
"x... | COMB | GEOM | COMPUTE | sympy | COMB1 | [
"COMB1/COUNT_SUM_EQUALS",
"COUNT_SUM_EQUALS"
] | 3e1adf | antilemma_sum_equals_v1 | null | 4 | 0 | [
"COMB1",
"COUNT_SUM_EQUALS"
] | 2 | 0.005 | 2026-02-08T15:39:27.513860Z | {
"verified": true,
"answer": 10774,
"timestamp": "2026-02-08T15:39:27.519281Z"
} | 61e2a9 | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 216,
"completion_tokens": 1476
},
"timestamp": "2026-02-24T18:22:16.555Z",
"answer": 10774
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COMB1",
"status": "ok"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "COUNT_SUM_EQUALS",
"status": "ok"
},
{
"lemma": "V7",
"status":... | {
"lo": -2.4,
"mid": 1.57,
"hi": 5.75
} | ||
6cd158 | comb_factorial_compute_v1_784195855_9015 | Let $n$ be the number of positive integers $p$ for which there exists a positive integer $q$ such that $p < q$, $\gcd(p, q) = 1$, and $pq = 1323000$. Let $Q$ be the remainder when $25043 \cdot n!$ is divided by $81393$. Compute $Q$. | 53,595 | graphs = [
Graph(
let={
"_n": Const(25043),
"n": CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), Var(name='q')), right=Const(value=1323000)), Eq(left=GCD(a=Var(name='p'), b=Var... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | comb_factorial_compute_v1 | null | 6 | 0 | [
"COPRIME_PAIRS"
] | 1 | 0.003 | 2026-02-08T16:28:43.659145Z | {
"verified": true,
"answer": 53595,
"timestamp": "2026-02-08T16:28:43.661681Z"
} | 71b43b | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 123,
"completion_tokens": 5792
},
"timestamp": "2026-02-17T05:28:51.932Z",
"answer": 53595
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "MOD_MUL",
"status": "no"
},
{
"lemma": "V5",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
ba7f9a | modular_inverse_v1_48377204_1799 | Let $m = 569$ and $a = 437$. Define $r$ to be the smallest positive integer $x$ such that $1 \leq x \leq 568$ and
$$
437x \equiv 1 \pmod{569}.
$$
Let $S$ be the set of all positive divisors $d$ of $9090$ such that $1 \leq d \leq 90$. Let $M$ be the largest element of $S$. Compute the remainder when $M - r$ is divided b... | 58,819 | graphs = [
Graph(
let={
"_n": Const(90),
"a": Const(437),
"m": Const(569),
"upper": Const(568),
"result": MinOverSet(set=SolutionsSet(var=Var("x"), condition=And(Geq(Var("x"), Const(1)), Leq(Var("x"), Ref("upper")), Eq(Mod(value=Mul(Ref("a"), Var("... | NT | null | EXTREMUM | sympy | MAX_DIVISOR | [
"MAX_DIVISOR"
] | ad1a9b | modular_inverse_v1 | negation_mod | 5 | 0 | [
"MAX_DIVISOR"
] | 1 | 0.051 | 2026-02-08T16:24:59.605629Z | {
"verified": true,
"answer": 58819,
"timestamp": "2026-02-08T16:24:59.656965Z"
} | cd2d21 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 161,
"completion_tokens": 1465
},
"timestamp": "2026-02-17T02:58:37.843Z",
"answer": 58819
},
... | 1 | [
{
"lemma": "DS2",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MAX_DIVISOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
},
{
"lemma": "V1",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
0f8d8c | nt_count_with_divisor_count_v1_1116507919_131 | Let $n$ be a positive integer such that $1 \leq n \leq 5297$ and the number of positive divisors of $n$ is exactly 8. Determine the number of such integers $n$. | 1,088 | graphs = [
Graph(
let={
"upper": Const(5297),
"div_count": Const(8),
"result": CountOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), Const(1)), Leq(Var("n"), Ref("upper")), Eq(NumDivisors(n=Var("n")), Ref("div_count"))))),
},
goal=Ref("re... | NT | null | COUNT | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | nt_count_with_divisor_count_v1 | null | 5 | 0 | [
"LIN_FORM"
] | 1 | 0.628 | 2026-02-08T02:26:33.630389Z | {
"verified": true,
"answer": 1088,
"timestamp": "2026-02-08T02:26:34.258804Z"
} | f5c3e7 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 13047
},
"timestamp": "2026-02-23T13:41:28.536Z",
"answer": 1087
},
{
... | 1 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K5",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "LTE_DIFF_P2",
"status": "no"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "MOD_SUB",
"status": "no"
}
] | {
"lo": 4.58,
"mid": 6.12,
"hi": 8.09
} | ||
a8f7de | nt_count_coprime_v1_238844314_907 | Let $n = 42$. Consider the set of all pairs $(x, y)$ of positive integers such that $x + y = n$. Let $P$ be the maximum value of $xy$ over all such pairs. Now consider the set of all pairs $(x, y)$ of positive integers such that $xy = P$. Let $k$ be the minimum value of $x + y$ over all such pairs. Compute the number o... | 13,330 | graphs = [
Graph(
let={
"_n": Const(42),
"upper": Const(46656),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), MaxOverSet(set... | NT | null | COUNT | sympy | B1 | [
"B1/B3"
] | 80b49d | nt_count_coprime_v1 | null | 6 | 0 | [
"B1",
"B3"
] | 2 | 4.129 | 2026-02-08T13:43:27.804783Z | {
"verified": true,
"answer": 13330,
"timestamp": "2026-02-08T13:43:31.933696Z"
} | d1fdb1 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 158,
"completion_tokens": 1332
},
"timestamp": "2026-02-15T20:43:57.483Z",
"answer": 13330
},
... | 1 | [
{
"lemma": "B1",
"status": "ok"
},
{
"lemma": "B3",
"status": "ok_later"
},
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_DIVISOR_COUNT",
"status": "no"
},
{
"lemma": "K15",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},... | {
"lo": -5.49,
"mid": 0.22,
"hi": 6.51
} | ||
5ea1d2 | nt_count_gcd_equals_v1_677425708_4084 | Let $d$ be the smallest divisor of $606685837$ that is at least $2$. Let $k = 151$ and let $N = 31329$. Compute the number of positive integers $n$ such that $1 \leq n \leq N$ and $\gcd(n, k) = d$. | 207 | graphs = [
Graph(
let={
"upper": Const(31329),
"k": Const(151),
"d": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(606685837))))),
"result": CountOverSet(set=SolutionsSet(var=Var("n"),... | NT | null | COUNT | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | nt_count_gcd_equals_v1 | null | 5 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 2.583 | 2026-02-08T06:25:18.305039Z | {
"verified": true,
"answer": 207,
"timestamp": "2026-02-08T06:25:20.887737Z"
} | 79a753 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 0,
"correct": {
"strict": false,
"boxed": false,
"relaxed": false
},
"usage": {
"prompt_tokens": 114,
"completion_tokens": 1714
},
"timestamp": "2026-02-12T23:49:59.789Z",
"answer": 0
},
{... | 0 | [
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_ADD",
"status": "n... | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
8197d4 | algebra_quadratic_discriminant_v1_677425708_2552 | Let $n = 4$, $a = 2$, and $c = -20$. Define $b$ to be the number of integers $t$ with $5 \leq t \leq 24$ for which there exist positive integers $a$ and $b$ such that $1 \leq a \leq 9$, $1 \leq b \leq 2$, and $t = 2a + 3b$. Compute $b^2 - 4ac$. | 484 | graphs = [
Graph(
let={
"_n": Const(4),
"a": Const(2),
"b": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const... | NT | null | COMPUTE | sympy | COPRIME_PAIRS | [
"LIN_FORM"
] | 7b2633 | algebra_quadratic_discriminant_v1 | null | 3 | 0 | [
"COPRIME_PAIRS",
"LIN_FORM"
] | 2 | 0.022 | 2026-02-08T05:07:09.902623Z | {
"verified": true,
"answer": 484,
"timestamp": "2026-02-08T05:07:09.924953Z"
} | 619f7b | CC BY 4.0 | [
{
"id": 2,
"model": "openai/gpt-oss-120b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 217,
"completion_tokens": 1245
},
"timestamp": "2026-02-11T22:57:37.560Z",
"answer": 484
},
{
"i... | 1 | [
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_FIB_DIVISIBLE",
"status": "no"
},
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_VAL",
"status": "no"
},
{
"lemma": "V5",
"status": "... | {
"lo": -7.01,
"mid": -4.68,
"hi": -2.15
} | ||
d7b785 | comb_sum_binomial_row_v1_677425708_3311 | Let $n$ be the smallest divisor of $1356277$ that is greater than or equal to $2$. Compute $2^n$. | 8,192 | graphs = [
Graph(
let={
"_n": Const(2),
"n": MinOverSet(set=SolutionsSet(var=Var("d"), condition=And(Geq(Var("d"), Const(2)), Divides(divisor=Var("d"), dividend=Const(1356277))))),
"result": Pow(Ref("_n"), Ref("n")),
},
goal=Ref("result"),
)
] | NT | null | SUM | sympy | MIN_PRIME_FACTOR | [
"MIN_PRIME_FACTOR"
] | bc3776 | comb_sum_binomial_row_v1 | null | 3 | 0 | [
"MIN_PRIME_FACTOR"
] | 1 | 0.001 | 2026-02-08T05:39:00.120775Z | {
"verified": true,
"answer": 8192,
"timestamp": "2026-02-08T05:39:00.121498Z"
} | 7f4280 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 76,
"completion_tokens": 506
},
"timestamp": "2026-02-12T12:14:43.956Z",
"answer": 8192
},
{
... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "K18",
"status": "no"
},
{
"lemma": "MIN_PRIME_FACTOR",
"status": "ok"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -3.44,
"mid": 1.34,
"hi": 6.56
} | ||
f68121 | sequence_fibonacci_compute_v1_1439011603_2281 | Let $n$ be the number of integers $t$ such that $27 \leq t \leq 102$ and there exist integers $a$ and $b$ with $1 \leq a \leq 2$, $1 \leq b \leq 10$, and $t = 21a + 6b$. Compute the value of $32761 - F_n$, where $F_n$ denotes the $n$th Fibonacci number. | 25,996 | graphs = [
Graph(
let={
"n": CountOverSet(set=SolutionsSet(var=Var("t"), condition=Exists(var=Var(name='a'), condition=Exists(var=Var(name='b'), condition=And(Geq(left=Var(name='a'), right=Const(value=1)), Leq(left=Var(name='a'), right=Const(value=2)), Geq(left=Var(name='b'), right=Const(value=1... | NT | null | COMPUTE | sympy | LIN_FORM | [
"LIN_FORM"
] | 7b2633 | sequence_fibonacci_compute_v1 | null | 4 | 0 | [
"LIN_FORM"
] | 1 | 0.005 | 2026-02-08T16:39:49.820982Z | {
"verified": true,
"answer": 25996,
"timestamp": "2026-02-08T16:39:49.825903Z"
} | 084856 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 140,
"completion_tokens": 961
},
"timestamp": "2026-02-17T10:07:06.907Z",
"answer": 25996
},
{... | 1 | [
{
"lemma": "L3c",
"status": "no"
},
{
"lemma": "LIN_FORM",
"status": "ok"
},
{
"lemma": "MAX_PRIME_BELOW",
"status": "no"
},
{
"lemma": "MOD_ADD",
"status": "no"
},
{
"lemma": "V3",
"status": "no"
},
{
"lemma": "V8",
"status": "no"
}
] | {
"lo": -7.08,
"mid": -0.29,
"hi": 6.49
} | ||
a2f263 | nt_count_gcd_equals_v1_1353956133_509 | Let $k$ be the minimum value of $x + y$ over all ordered pairs $(x,y)$ of positive integers such that $xy = 5184$. Let $U = 45796$. Determine the number of positive integers $n$ such that $1 \le n \le U$ and $\gcd(n, k) = 48$. Compute the remainder when $11603$ times this count is divided by $65521$. | 41,156 | graphs = [
Graph(
let={
"upper": Const(45796),
"k": MinOverSet(set=MapOverSet(set=SolutionsSet(var=Tuple(elements=[Var("x"), Var("y")]), condition=And(IsPositive(arg=Var(name='x')), IsPositive(arg=Var(name='y')), Eq(Mul(Var("x"), Var("y")), Const(5184)))), expr=Sum(Var("x"), Var("y")... | NT | null | COUNT | sympy | B3 | [
"B3"
] | 0cd20d | nt_count_gcd_equals_v1 | null | 4 | 0 | [
"B3"
] | 1 | 6.892 | 2026-02-08T11:29:00.069314Z | {
"verified": true,
"answer": 41156,
"timestamp": "2026-02-08T11:29:06.961051Z"
} | 12c7c8 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 138,
"completion_tokens": 1071
},
"timestamp": "2026-02-14T14:51:28.286Z",
"answer": 41156
},
... | 1 | [
{
"lemma": "B3",
"status": "ok"
},
{
"lemma": "COUNT_PRIMES",
"status": "no"
},
{
"lemma": "K14",
"status": "no"
},
{
"lemma": "K17",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"status": "no"
}
] | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} | ||
44a1e8 | antilemma_cartesian_v1_1820931509_667 | Let $x$ be the number of ordered pairs $(i,j)$ such that $1 \leq i \leq 39$ and $1 \leq j \leq 48$. Compute the remainder when $24473 \cdot x$ is divided by $80614$. | 24,704 | graphs = [
Graph(
let={
"x": CountOverSet(set=CartesianProduct(left=IntegerRange(start=Const(1), end=Const(39)), right=IntegerRange(start=Const(1), end=Const(48)))),
"_c": Const(24473),
"Q": Mod(value=Mul(Ref("_c"), Ref("x")), modulus=Const(80614)),
},
goa... | COMB | GEOM | COMPUTE | sympy | COUNT_CARTESIAN | [
"COUNT_CARTESIAN"
] | 409d7d | antilemma_cartesian_v1 | null | 2 | 0 | [
"COUNT_CARTESIAN"
] | 1 | 0.001 | 2026-02-08T11:49:21.576988Z | {
"verified": true,
"answer": 24704,
"timestamp": "2026-02-08T11:49:21.577815Z"
} | 81de63 | CC BY 4.0 | [
{
"id": 1,
"model": "openai/gpt-oss-20b",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 170,
"completion_tokens": 1528
},
"timestamp": "2026-02-24T14:48:48.555Z",
"answer": 24704
},
{
"... | 1 | [
{
"lemma": "C2",
"status": "no"
},
{
"lemma": "COUNT_CARTESIAN",
"status": "ok"
},
{
"lemma": "COUNT_COPRIME_GRID",
"status": "no"
},
{
"lemma": "COUNT_INTEGER_RANGE",
"status": "no"
},
{
"lemma": "V7",
"status": "no"
},
{
"lemma": "V8_SUM",
"statu... | {
"lo": -2.35,
"mid": 1.22,
"hi": 4.84
} | ||
22101a | nt_max_prime_below_v1_1520064083_8967 | Let $P$ be the set of all positive integers $p$ for which there exists a positive integer $q$ such that $pq = 24$, $\gcd(p, q) = 1$, and $p < q$. Let $k$ be the number of elements in $P$. Define $S$ to be the set of all prime numbers $n$ such that $k \le n \le 20449$. Determine the maximum value in $S$. | 20,443 | graphs = [
Graph(
let={
"upper": Const(20449),
"result": MaxOverSet(set=SolutionsSet(var=Var("n"), condition=And(Geq(Var("n"), CountOverSet(set=SolutionsSet(var=Var("p"), condition=And(IsPositive(arg=Var(name='p')), Exists(var=Var(name='q'), condition=And(Eq(left=Mul(Var(name='p'), V... | NT | null | EXTREMUM | sympy | COPRIME_PAIRS | [
"COPRIME_PAIRS"
] | 2bb3aa | nt_max_prime_below_v1 | null | 5 | 0 | [
"COPRIME_PAIRS"
] | 1 | 1.139 | 2026-02-08T10:27:22.643391Z | {
"verified": true,
"answer": 20443,
"timestamp": "2026-02-08T10:27:23.782095Z"
} | 9a02c9 | CC BY 4.0 | [
{
"id": 5,
"model": "deepseek-ai/DeepSeek-V3.2",
"score": 3,
"correct": {
"strict": true,
"boxed": true,
"relaxed": true
},
"usage": {
"prompt_tokens": 144,
"completion_tokens": 2223
},
"timestamp": "2026-02-14T07:30:16.711Z",
"answer": 20443
},
... | 1 | [
{
"lemma": "COPRIME_PAIRS",
"status": "ok"
},
{
"lemma": "K13",
"status": "no"
},
{
"lemma": "K16",
"status": "no"
},
{
"lemma": "MOD_FACTORIAL",
"status": "no"
},
{
"lemma": "POLY_PADIC_VAL_CONST",
"status": "no"
},
{
"lemma": "VAL_SUM_EQ",
"statu... | {
"lo": -5.14,
"mid": 0.32,
"hi": 6.51
} |
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