The board / number theory / #681
Erdős Problem #681
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).
`IsLPF p m` says that `p` is the least prime factor of `m`.
**Erdős problem 681.** Is it true that for all large \(n\) there exists \(k\) such that \(n + k\) is composite and \(p(n+k) > k^2\), where \(p(m)\) 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/681.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA389680
Original pageerdosproblems.com/681
Attempts
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Live Erdős Problems #681 page status is OPEN, but it lists “Currently working on this problem: stellachenyl” (accessed 2026-07-27), so the mandatory no-collision rule applies.
SKIPPED