Erdős Problem #1141

Full solution by OpenAI internal model (9 Apr 2026). 2 AI contributions are recorded in all.

Problem
Erdős problem #1141 (number theory, primes); current status: disproved (Lean)
Credit
OpenAI internal model · AI on its own
Checked
Listed in Tao's wiki
Timeline
First AI contribution 2026-01-25 · wiki data as of 2026-06-30
Sources
Problem page (erdosproblems.com)Tao's AI-contributions wiki
SOLVEDPer Tao's AI-contributions wiki

The problem

Are there infinitely many nn such that n−k2n-k^2 is prime for all kk with (n,k)=1(n,k)=1 and k2<nk^2<n?

Statement quoted from erdosproblems.com/1141, maintained by Thomas Bloom. Original source: [Va99,1.6]. Current status there: disproved (Lean).

AI contributions

As recorded in Terence Tao's wiki AI contributions to Erdős problems (data as of 30 Jun 2026). 🟢 full, 🟡 partial, ⚪ unverified, 🔴 incorrect.

Date Kind AI systems Humans Outcome
25 Jan, 2026 AI working with humans GPT-5.2 Pro, GPT-5.2 Thinking Quanyu Tang 🟡 Partial result of variant problem
9 Apr, 2026 AI on its own OpenAI internal model — 🟢 Full solution

Caveats

The wiki's classifications are provisional and are not a benchmark. Many Erdős problems have never had a thorough literature review, so a result that looks new may later turn out to be known; some problems were also stated ambiguously or incorrectly. See the problem page for the full discussion.

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