Erdős problem 1201 · problems.science

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 $m$ ? A short argument via the Matomäki-Radziwiłł theorem establishes the lower-density version.

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1201.lean

Retained formal statement1 of 2

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 $m$ )?

FormalConjectures/ErdosProblems/1201.leanErdos1201.erdos_12013 linesExact file

1True ↔2  ∀ ε > 0,3    ∀ 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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