OPEN
This is open, and cannot be resolved with a finite computation.
Are there infinitely many $n$ such that $n-k^2$ is prime for all $k$ with $(n,k)=1$ and $k^2<n$?
In
[Va99] it is asked whether $968$ is the largest integer with this property, but this is an error, since for example $968-9=7\cdot 137$.
The list of $n$ satisfying the given property is
A214583 in the OEIS. The largest known such $n$ is $1722$.
ChatGPT and Tang
have shown that the number of such $n$ in $[1,N]$ is at most $N^{1/2+o(1)}$.
See also
[1140] and
[1142].
View the LaTeX source
This page was last edited 26 January 2026.
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T. F. Bloom, Erdős Problem #1141, https://www.erdosproblems.com/1141, accessed 2026-03-01
