Erdős Problem #454 — If $f(n)$ denotes $\min_i (p_{n+i} + p_{n-i})$ , is it true that …

If $f(n)$ denotes $\min_i (p_{n+i} + p_{n-i})$ , is it true that

\limsup_n (f(n) - 2p_n) = \infty\,?

References

Primary source

Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathématique 28 (1980).

Posted 1 month ago

Refreshed 1 month ago

Open

The problem remains open: recent discussion about sums involving neighboring primes reports no proof or disproof.

Erdős problem #454 concerns a $\limsup$ question about symmetric sums of neighboring primes. The register currently labels the problem open.

August 2026 discussion

On August 19, the register noted that the discussion thread had moved, but reported no new proof, disproof, or status change.

Current status (as of August 2026): The problem remains open; discussion has increased, but no proof, disproof, or status change is recorded.

Sources

No solutions have been posted yet.