Erdős Problem #1141

The problem

Are there infinitely many $n$ such that $n-k^2$ is prime for all $k$ with $(n,k)=1$ and $k^2<n$?

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.

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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