Bounded prime gaps:
Write . Announced on 1 September 2026: , building on Stadlmann's of the previous day.
- Result
- Proved(see note)
- Status
- Candidate (review pending)
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Analytic number theory
- Posed by
- Alphonse de Polignac (the twin prime conjecture); the bounded form since Goldston, Pintz and Yıldırım
- Year posed
- 1849
- Years open
- 177y
- Solved
- 2026-09-01
- Model
- unspecified AI agents
- Vendor
- —
- Collaborators
- Shiva Kintali
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 62 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
, between Stadlmann's of 31 August and Axiom Math's of 3 September. Superseded within two days, which Kintali noted himself.
What the AI did
Kintali's own words on X: "I showed that H1 <= 236 with the help of AI, building on Julia Stadlmann's work." He describes the method as the GPY approach with the Maynard-Tao sieve, and says he then stopped his AI agents and moved to another problem. That is the whole of the public disclosure: no model is named, the division of labour is not described, and there is no preprint.
Verification
No independent mathematician has checked this yet. The thinnest source of the three 2026 bounded-gaps entries, and recorded as Candidate for that reason. An announcement on X with no preprint, no named model and no argument in public. It is recorded because a bound is a bound and this one held the record for two days between Stadlmann's 240 and Axiom Math's 212; it is not recorded as settled. If a preprint appears, this entry should be revisited.
Sources
- Independent workStadlmann's 240, the bound this improves on
- OtherShiva Kintali on X
FrontierStep on Bounded prime gaps · · a step on the frontier, since improved