Erdős problem 457 · problems.science

Is there some $\epsilon > 0$ such that there are infinitely many $n$ where all primes $p \le (2 + \epsilon) \log n$ divide $\prod_{1 \le i \le \log n} (n + i)?$

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FormalConjectures/ErdosProblems/

457.lean

Retained formal statement3 of 3

More generally, let $q(n, k)$ denote the least prime which does not divide $\prod_{1 \le i \le k}(n + i)$ . This problem asks whether $q(n, \log n) \ge (2 + \epsilon) \log n$ infinitely often.

FormalConjectures/ErdosProblems/457.leanErdos457.erdos_457.variants.qnk1 lineExact file

1sorry ↔ ∃ ε > 0, {n | (2 + ε) * Real.log ↑n ≤ ↑(Erdos457.q n (Real.log ↑n))}.Infinite

OpenStatement only, no proof

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