What was already known
Rankin’s bound had one log₂ X factor. The Ford–Green–Konyagin–Maynard–Tao and earlier tilted-sieve bounds were weaker asymptotically than this claim.
AI involvement
The paper credits GPT 6 Astra with the mathematical proof. The repository reports an initial autonomous formalization pass followed by human-guided quality edits.
The manuscript directly assigns the proof to GPT 6 Astra, and the proof-artifact metadata describes an initial autonomous agent pass.
Importance
The proposed bound improves a longstanding asymptotic lower-bound line for prime gaps.
Limitations
The formalization metadata identifies the matched theorems and describes its review as self-assessed. No completed human proof check is documented, and the expected optimal gap order remains open.
Technical verification
The repository reports a complete Lean 4 formalization of Theorem 1.1 and Proposition 1.2, with a comparator statement for indexed consecutive primes, no sorry and only standard axioms.
Formal checking
Lean proofs long_gap_theorem, short_translates and long_prime_gaps with Comparator statement alignment
- Checker
- OpenAI LongGapsBetweenPrimes Lean 4 development
- Scope
- Paper Theorem 1.1 and Proposition 1.2, including indexed-prime main theorem
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
No named human explains the central reciprocal-logarithm weight and short-translates proof; Few is the evidence default.
Correction and publication history
The proposed bound improves a longstanding asymptotic lower-bound line for prime gaps.
Read this published revision