The board / number theory / #462
Erdős Problem #462
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Let \(p(n)\) denote the least prime factor of \(n\). Is there a constant \(C>0\) such that \[\sum_{x\leq n\leq x+C\sqrt{x}(\log x)^2}\frac{p(n)}{n}\gg 1\] for all sufficiently large \(x\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/462.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA032742
Original pageerdosproblems.com/462
Attempts
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The stronger composite-only inequality with C=1 is certified (>0.961) for every real x in [10^6,10^9], and the remaining all-x asymptotic step is the stated uniform balanced-semiprime Type-II lower bo
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