OPEN
This is open, and cannot be resolved with a finite computation.
Let\[f(n) = \min_{i<n} (p_{n+i}+p_{n-i}),\]where $p_k$ is the $k$th prime. Is it true that\[\limsup_n (f(n)-2p_n)=\infty?\]
Pomerance
[Po79] has proved the $\limsup$ is at least $2$.
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This page was last edited 07 October 2025.
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