The board / number theory / #1139
Erdős Problem #1139
OPENdatabase updated 2026-01-23
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 \(1\leq u_1 < u_2 < \cdots\) be the sequence of integers with at most \(2\) prime factors. Is it true that \[\limsup_{k \to \infty} \frac{u_{k+1}-u_k}{\log k}=\infty?\]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1139.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1139
Attempts
submit one →Strong partial, verified — not closed by us (Price's claimed proof is unauditable).
PARTIAL