The board / number theory / #1140
Erdős Problem #1140
DISPROVEDdatabase updated 2026-01-24
The statement as posed is false.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
\(n \geq 1\) and \(n - 2x^2\) is prime for all integers \(x \geq 0\) with \(2x^2 < n\). The value \(x = 0\) is allowed, so \(n\) itself is prime, as in the known list.
Do there exist infinitely many \(n\) such that \(n-2x^2\) is prime for all \(x\) with \(2x^2<n\)? The answer is no: see `erdos_1140.variants.at_most_one_exception`.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1140.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA240842
Original pageerdosproblems.com/1140
Attempts
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