[{"data":1,"prerenderedAt":4},["ShallowReactive",2],{"xb9ZMy45Ua":3},"[![](logo.svg)](https://axiommath.ai/)\n\n# PrimeGapsLib\n\nPublic Lean library for formalizations related to prime gaps, maintained by Axiom Math.\n\n## Dependencies\n\nThis repository depends on [an internal fork of PrimeNumberTheoremAnd](https://github.com/AxiomMath/PrimeNumberTheoremAnd) (original [here](https://github.com/AlexKontorovich/PrimeNumberTheoremAnd)), changed to use the module system.\n\n## Structure\n\n* [PrimeGaps](PrimeGaps/): the main library combining [PrimeGapsTheory](PrimeGapsTheory/) and [PrimeGapsCert](PrimeGapsCert/).\n* [PrimeGapsTheory](PrimeGapsTheory/): the main formalization excluding large numerical computations, which builds quickly.\n* [PrimeGapsCert](PrimeGapsCert/): large numerical computations that might take a long time to build.\n\n## Main Results\n\n1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in [PrimeGaps.Bounded246](PrimeGaps/Bounded246.lean).\n2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in [PrimeGapsTheory.Endgame.Main](PrimeGapsTheory/Endgame/Main.lean).\n3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in [PrimeGapsTheory.Gap246.Endgame.Main](PrimeGapsTheory/Gap246/Endgame/Main.lean).\n\nFormal versions of these statements can be found in the formal challenge described in [§Comparator](#comparator).\n\n## Comparator\n\nA formal challenge that is self-contained and only depends on Mathlib is located in [Comparator.Challenge](Comparator/Challenge.lean). It contains statement 1 of [§Main Results](#main-results) with `sorry` as proof.\n\nThis repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install `comparator`. Then, run the following command:\n```\nlake env comparator Comparator/comparator.json\n```\nBeware that this can take hours.\n\nThe proofs of statements 2 and 3 of [§Main Results](#main-results) compile much faster, so we also included a formal challenge for them in [Comparator.ChallengeFast](Comparator/ChallengeFast.lean). To verify this repository against this challenge file, run the following command:\n```\nlake env comparator Comparator/comparator_fast.json\n```\nThis should only takes minutes.\n",1789154821931]