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An Astra-attributed preprint lowers the bounded prime-gap record to 186

An OpenAI preprint proves DHL[40,2] and concludes that infinitely many pairs of consecutive primes differ by at most 186, improving the long-standing published bound of 246 and a concurrent 240 result.

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Stable ID
math-prime-gap-186-bound-2026
Revision
math-prime-gap-186-bound-2026.v1
Field
Mathematics · Analytic number theory, sieve methods and formal verification
Evidence
Tier 1 · Peer reviewed: No
Record state
Provisional · Provisional claimed theorem; conditional formalization
Last checked

AI role

The paper attributes the proof to GPT-6 Astra. OpenAI supplied a conditional Lean development and a Python-FLINT numerical certificate; no independent human semantic review was located.

Record details

Problem or result
The best unconditional upper bound for the limit inferior of consecutive-prime gaps
Authors
OpenAI; proof attributed to GPT-6 Astra
Institutions
OpenAI
Result date
Paper dated August 30, 2026; publicly announced September 3, 2026

Why it matters

Bounded prime gaps are a central post-Zhang problem in analytic number theory. A correct 186 bound would be the first improvement below 246 in more than a decade and a striking AI-assisted advance.

Limits

The result is an unreviewed preprint. Its Lean derivation remains conditional on three explicit input axioms, including cited finite-field estimates and numerical integral/cap bounds; the numerical certificate does not discharge those axioms. The twin-prime gap of two remains unproved.

Sources

  1. Primary: OpenAI, GPT-6 Astra research announcement
  2. Primary: OpenAI, Improved Short Gaps Between Primes
  3. Artifacts: Conditional Lean development and numerical certificate

Correction and revision history

  1. 2026-09-07 — Added after primary-source, scope, status, AI-role and limitation review.

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