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Erdős problem 1201

Is it true that for every ϵ,η>0\epsilon,\eta>0 there exists a kk such that the density of nn for which P(n(n+1)⋯(n+k))>n1−ϵP(n(n+1)\cdots(n+k))>n^{1-\epsilon} is at least 1−η1-\eta, where P(m)P(m) is the greatest prime divisor of mm? A short argument via the Matomäki-Radziwiłł theorem establishes the lower-density version.

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Retained declaration

FormalConjectures/ErdosProblems/1201.lean

Formal Conjectures

FormalConjectures/ErdosProblems/1201.leanErdos1201.erdos_12013 linesExact file
True ↔  ∀ ε > 0,    ∀ η > 0, ∃ k, Filter.liminf (fun x => ↑↑(Nat.count (Erdos1201.Erdos1201Set ε k) x) / ↑↑x) Filter.atTop ≥ 1 - η
OpenStatement only, no proof

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  • AI collaborating with humans

    Erdős AI contributions wiki · 30 Apr, 2026

    Machine
    GPT-5.5 Pro
    People
    Przemek Chojecki
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  • argument

    VibeMathed

    Machine
    GPT-5.5 Pro
    People
    Przemysław Chojecki
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    partial
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