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 Gaps ≤186 in Lean as Records Fall in Days(22 posts)→
More from Models
- GPT-6 Astra and Claude Fable 5.1 write $10,000 research papers — experts reject all — sayashk · 2026-10-21
- GitHub Copilot's HydraFusion Orchestrates Multiple Models Per Task — WirelessLife · 2026-10-21
- OpenVLHarness turns any MLLM into a visual reasoner, +9.9 points across 22 datasets — yining_hong · 2026-10-21
- User claims Gemini analyzed his tennis match video and improved his game — zacharynado · 2026-10-21
- Opus 5.5 tops OpenRouter spending in 20 of 29 task categories — mmurph · 2026-10-21
- Meta team builds open-source 30B LLM from scratch in months, hails 'second era' — TimDarcet · 2026-10-21