GPT-6 pushes twin prime bound to 186 in Lean-verified proof, days after human and rival AI records
新智元 · wechat · 2026-09-04
OpenAI announced that GPT-6 (Astra) improved the best known bound on the twin prime gap from 246 to 186, releasing a Lean4-formalized proof in the open-source PrimeGaps186 repo.
- Record timeline: Yitang Zhang's 70M bound (2013) was cut to 246 by the Polymath project; Julia Stadlmann hit 240 on Aug 31, Axiom's Prover claimed 212 on Sep 3, and OpenAI's 186 followed hours later.
- Method: GPT-6 introduced a new "triple-dense divisibility" condition relaxing smooth-modulus restrictions, expanded sieve weight support, and built a 40-element admissible set of diameter 186.
- Verification: fully executable Lean4 code plus numerical certificates; however, three input axioms on exponential sums (backed by known results like Deligne's theorem) remain unformalized, making the proof conditional.
- CoT traces: the model rejected shortcuts, switched from floats to exact rational arithmetic, and escaped a dead-end 41-dimensional optimization with an asymmetric density strategy in 40 dimensions.
Mathematicians including Su Weijie, Tony Feng, and Ken Ono hailed it as a landmark for AI4Math, though the path to the ultimate bound of 2 remains long.
Related event: GPT-6-Astra Proves Prime Gaps ≤186 in Lean as Records Fall in Days(22 posts)→
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