OpenAI published a Lean 4 formalization of prime gaps ≤ 186, conditional on three unproven axioms.

openai/PrimeGaps186, created September 2 under Apache-2.0, at 117 stars, formalizes lim inf(p_{n+1} - p_n) ≤ 186 via the Dickman-Hardy-Littlewood conjecture applied to a 40-element admissible tuple. It proves three theorems but remains conditional on a Kloosterman3 bound from Deligne, a Kloosterman2 correlation bound from Fouvry-Kowalski-Michel 2013, and 104 outer plus 45 inner integral bounds verified only numerically. A Python certificate ships for the numerical part. The honest framing is a conditional machine-checked result. GitHub