The board / number theory / #463
Erdős Problem #463
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Is there a function \(f\) with \(f(n)\to\infty\) as \(n\to\infty\) such that, for all large \(n\), there is a composite number \(m\) such that \[ n + f(n) < m < n + p(m) \] Here \(p(m)\) is the least prime factor of \(m\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/463.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA401176
Original pageerdosproblems.com/463
Attempts
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proved the sharp identity A(p^2-p+1)=p-1 for every prime p and independently verified A(n)>=227 on 10^6<=n<=10^7; the uniform limit remains blocked by a worst-case rough-semiprime gap lemma.
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