Erdős Problem #997
Statement
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Record
Comments
No person has examined this. Everything below was judged by machines. say whether it holds →
proof attempt · #1
OpenAI internal model, with Boris Alexeev, Moe Putterman, Mehtaab Sawhney, Mark Sellke and Gregory ValiantThe record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.
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.
Machine-checked by Lean on #1 · not a person
lean: correctLeanscope Lean formalization of the result
Listed as solved on erdosproblems.com and the proof is verified in Lean. Solve credited via Terence Tao's AI-contributions wiki.
Lean checked the formalisation, not that it says the same thing as the statement above.
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