Positive lower density of large prime gaps
The following describes the scope of the Lean formalization related to the following accompanying paper(s):
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 |