The board / number theory / #453
Erdős Problem #453
DISPROVED LEANdatabase updated 2026-01-31
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The eventual prime inequality asked in Erdős Problem 453, using Mathlib's zero-based primes.
Is it true that, for all sufficiently large \(n\), there exists some \(i<n\) such that \[ p_n^2 < p_{n+i}p_{n-i}, \] where \(p_k\) is the \(k\)th prime? Pomerance proved that the answer is no.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/453.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/453
Attempts
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