The board / number theory / #932
Erdős Problem #932
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).
Let \(p_k\) denote the \(k\)th prime. For infinitely many \(r\) there are at least two integers \(p_r < n < p_{r+1}\) all of whose prime factors are \(< p_{r + 1} - p_r\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/932.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA387864
Original pageerdosproblems.com/932
Attempts
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Live page status is OPEN with 0 claimed proofs, but “Currently working on this problem” lists lof310 (accessed 2026-07-28), so the mandated collision-avoidance rule forbids an attempt.
SKIPPED