PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

- PrimeGapsTheory: the main formalization excluding large numerical computations, which builds quickly.
- PrimeGapsCert: large numerical computations that might take a long time to build.
- PrimeGaps: the main library combining PrimeGapsTheory and PrimeGapsCert.

Main Results

• The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often: PrimeGapsTheory/Endgame/Main.lean.
• The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often: PrimeGapsTheory/Gap246/Endgame/Main.lean.
• The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often: [TODO].

Comparator

This repository can be verified with the Lean comparator on a Linux machine by following the instructions in https://github.com/leanprover/comparator and then running the following command:

lake env comparator Comparator/comparator.json

This skips the numerical certificate which can take a long time.