VibeMathedMath problems solved with AI

Erdős Problem #793

Erdős problem #793 · erdosproblems.com/793

Let F(n)F(n) be the largest A⊆{1,…,n}A\subseteq\{1,\dots,n\} with a∤bca\nmid bc for distinct a,b,c∈Aa,b,c\in A. Is F(n)=π(n)+(C+o(1)) n2/3(log⁡n)−2F(n)=\pi(n)+(C+o(1))\,n^{2/3}(\log n)^{-2} for some constant CC?

Result
Proved
Status
Resolved
AI contribution
AI-discovered
Method
Argument
Field
Number Theory
Posed by
Paul Erdős
Year posed
1969
Years open
57y
Solved
2026-07
Model
GPT-5.6 Sol
Vendor
OpenAI
Collaborators
Przemek Chojecki
Verification
Lean-verified
Publication
Announced
Significance
10 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

GPT-5.6 Sol (prompted by Przemek Chojecki) proved F(n)=π(n)+(272+o(1))n2/3(log⁡n)2F(n)=\pi(n)+(\tfrac{27}{2}+o(1))\frac{n^{2/3}}{(\log n)^2}, a refined form of Erdős's 1938 argument.

Verification

Marked proved (Lean) on erdosproblems.com via a proof claim by GPT-5.6 Sol.

Source

Changelog2 changes
  • loader3229changed Verification from “site-confirmed” to “lean-verified”, also Verification note
  • Curatoradded this entry

Discussion