The board / number theory / #370
Erdős Problem #370
PROVED LEANdatabase updated 2025-11-24
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 the largest prime factor of \(n\) is \(< n^{\frac{1}{2}}\) and the largest prime factor of \(n + 1\) is \(< (n + 1)^{\frac{1}{2}}\). Steinerberger has pointed out this problem has a trivial solution. This was formalized in Lean by Alexeev using Aristotle.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/370.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/370
Attempts
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