OpenAI open-sources PrimeGaps186, a Lean formalization of a prime-gap bound of 186
johnowhitaker · x · 2026-09-04
OpenAI published PrimeGaps186 on GitHub: a Lean 4 formalization targeting liminf(p{n+1}-pn) ≤ 186 for consecutive primes. The development derives DHL[40,2] — every admissible set of 40 integer shifts has infinitely many translates containing at least two primes — but remains conditional on three explicit input axioms, since the cited estimates and numerics are not yet Lean proofs. The repo includes a Python numerical certificate, comparator code, and results PDF.
Related event: GPT-6-Astra Proves Prime Gaps ≤186 in Lean as Records Fall in Days(22 posts)→
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