| # Positive lower density of large prime gaps | |
| The following describes the scope of the Lean formalization related to the following accompanying paper(s): | |
| - [Positive lower density of large prime gaps](../../preprints/Positive-lower-density-of-large-prime-gaps-September-25-2026/main.pdf) | |
| ## Scope | |
| The formalized supplement proves that the indices $n$ for which $p_n/n<p_{n+1}/(n+1)$ have positive lower asymptotic density, where $p_n$ is the $n$th prime. Thus the normalized prime sequence has a positive-density set of increases. This is the prime-ratio corollary associated with the paper's theorem on a positive lower density of large prime gaps. | |
| ## Comparator links | |
| | Result | Comparator statement | | |
| | --- | --- | | |
| | Positive lower density of prime-ratio increases | [PrimeGaps.lean](../ComparatorChallenges/PrimeGaps.lean) | | |