GPT-6 Astra Pushes Bounded Prime Gaps Record from 246 to 186 with Lean Verification
机器之心 · wechat · 2026-09-04
OpenAI researcher Su Weijie announced that GPT-6 Astra improved the bounded gaps between primes upper bound from 246 to 186, with a Lean-formalized proof published as 'Improved Short Gaps Between Primes.'
- Context: The record fell from Zhang Yitang's 70 million (2013) through Maynard–Tao sieve improvements to 246. The model found new factorization conditions and expanded Maynard–Tao/Selberg sieve weights — searching proof combinations humans hadn't tried. OpenAI open-sourced the Lean 4 project.
- Same-day race: Axiom claimed a 212 bound; Anthropic said Claude previously formalized 188.
- Twist: Human mathematician Julia Stadlmann's independent 240 result surprised people precisely because it was AI-free — a sign of how quickly AI is expected in frontier math research.
Related event: GPT-6-Astra Proves Prime Gaps ≤186 in Lean as Records Fall in Days(22 posts)→
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