The board / number theory / #248
Erdős Problem #248
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Are there infinitely many \(n\) such that \(\omega(n + k) \ll k\) for all \(k \geq 1\)? Here \(\omega(n)\) is the number of distinct prime divisors of \(n\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/248.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/248
Attempts
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