What was already known
The a=1 problem was open. Pollack’s theorem on small prime quadratic residues supplies a pre-existing input; an earlier a=2 result omitted the coprimality condition.
AI involvement
An internal OpenAI model found the a=1 proof. Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke and Gregory Valiant report checking and explaining it, then initiated the fixed-a extension.
The model produced the original proof; the prompted extension has explicit human direction and is outside this entry's core scope.
Importance
The deduction settles the original Erdős prime-pattern question.
Limitations
The paper also proves a fixed-a extension after the authors proposed it and prompted ChatGPT; that extension has separate human direction and is outside this claim.
Technical verification
The coauthors report verifying each model solution, including this one; no machine check is documented. The maximal-n=1722 observation is only computational evidence and is not part of the finiteness theorem's check.
Independent checking
human verification of the solution before the independent ChatGPT attempts
- Checker
- Alexeev, Putterman, Sawhney, Sellke and Valiant
- Scope
- Model's a=1 finiteness proof for Problem 1141
- Basis
- Reported by the linked checker
Human understanding
The authors identified and explained the Pollack-based mechanism and recognized its fixed-a extension.
Correction and publication history
The deduction settles the original Erdős prime-pattern question.
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