The board / number theory / #1201
Erdős Problem #1201
OPENdatabase updated 2026-04-04
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).
The set of \(n\) for which \(P(n(n+1)\cdots(n+k)) > n^{1-\epsilon}\), where \(P(m)\) is the greatest prime divisor of \(m\).
Is it true that for every \(\epsilon,\eta>0\) there exists a \(k\) such that the density of \(n\) for which \(P(n(n+1)\cdots(n+k))>n^{1-\epsilon}\) is at least \(1-\eta\) (where \(P(m)\) is the greatest prime divisor of \(m\))?
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/1201.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1201
Attempts
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Live-page status is OPEN with 0 formal proof claims and no current worker, but the 30 April 2026 discussion explicitly claims a Matomäki–Radziwiłł proof, links a solution note, and includes a later “s
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