Erdős Problem #997
Erdős problem #997 · erdosproblems.com/997
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Analysis, Discrepancy, Primes
- Posed by
- Paul Erdős
- Year posed
- 1964
- Years open
- 62y
- Solved
- 2026-03-31
- Model
- OpenAI internal model
- Vendor
- —
- Collaborators
- Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke, Gregory Valiant
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 11 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
From "Short proofs in combinatorics and number theory": "In each case, the proof is due entirely to an internal model at OpenAI. The role of the human authors was simply to digest the proofs and modify the write-ups for clarity and elegance." This entry's solve is that paper's Theorem 4.1, proving that for every real alpha the sequence of fractional parts of alpha times the primes is not well-distributed.
Verification
Listed as solved on erdosproblems.com and the proof is verified in Lean. Solve credited via Terence Tao's AI-contributions wiki.
Sources
- PaperShort proofs in combinatorics and number theory (Section 4)
- Problem recorderdosproblems.com