Problem Statement
Let\[f(n) = \min_{i<n} (p_{n+i}+p_{n-i}),\]where $p_k$ is the $k$th prime. Is it true that\[\limsup_n (f(n)-2p_n)=\infty?\]
Categories:
Number Theory Primes
Progress
Pomerance [Po79] has proved the $\limsup$ is at least $2$.Source: erdosproblems.com/454 | Last verified: January 15, 2026