Let (p_k)_k≥ 1 be the sequence of primes in increasing order. For each integer n≥ 2, define f(n)=min_1≤ i<n(p_n+i+p_n-i). Is it true that limsup_n→∞bigl(f(n)-2p_n bigr)=∞?

Erdős problem #454

Let $(p_k)_{k\ge 1}$ be the sequence of primes in increasing order. For each integer $n\ge 2$ , define $f(n)=\min_{1\le i<n}(p_{n+i}+p_{n-i})$ . Is it true that $\limsup_{n\to\infty}\bigl(f(n)-2p_n\bigr)=\infty$ ?

Progress summary

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

erdosproblems.com

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Erdős Problems

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Erdős problem #454 — Erdős Problems

number-theory prime-numbers

2 days ago

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