GPT-6 Astra pushes twin prime gap bound from 246 down to 186
量子位 · wechat · 2026-09-04
- OpenAI's first GPT-6 Astra research result: a paper (with Lean 4 formal proof) improves the bound on consecutive prime gaps from 246 to 186, building on the Zhang Yitang → Polymath → Maynard/Tao lineage.
- Astra's breakthrough exploits triple-dense divisibility moduli previously considered intractable: complementary factorization conditions on D and E make the LCM triple-dense, enabling larger sieve support sets, verified independently with Python-FLINT.
- Mathematician Bartosz Naskręcki calls it a "quantum leap" — real-time Lean verification while conversing with the model.
- 3D demos are viral: photo-to-Blender villa running at 60fps, a Manhattan built in UE5 in a week, and Ethan Mollick's autonomous Alexandria Library historical simulation.
- Codex 0.153.1 adds searchable notes across context windows, replacing lossy compression; Schmidhuber, as usual, claims priority via his 2015 paper.
Related event: GPT-6-Astra Proves Prime Gap Bound of 186 in Lean, Open-Sourced by OpenAI(18 posts)→
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