What was already known
Classical and later constructions found arbitrarily large individual gaps, but those maximum-gap results did not establish a positive proportion above every fixed multiple of the average scale.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Changes the frequency known for large consecutive prime gaps, beyond existence of isolated examples.
Limitations
The pinned Lean scope note formalizes a prime-ratio corollary, not this full prime-gap-frequency theorem. No complete check of the main theorem is documented here.
Technical verification
Only the prime-ratio corollary is identified as formalized; the main prime-gap-frequency theorem lacks a documented complete check.
Formal checking
The pinned Lean scope note covers only the associated positive-density prime-ratio corollary.
- Checker
- OpenAI-reported Lean 4 / Comparator
- Scope
- The pinned Lean scope note covers only the associated positive-density prime-ratio corollary.
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, prior-work, and scoped checking review for non-notifying local inclusion.
Read this published revision