Erdős problem 889 · problems.science

Let $v(n,k)$ count the prime factors of $n+k$ which do not divide $n+i$ for $0\leq i < k$ . Is it true that $v_0(n)=\max_{k\geq 0}v(n,k)\to \infty$ as $n\to \infty$ ?

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5 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

889.lean

Retained formal statement2 of 5

Let $v_l(n) = \max_{k\geq l} v(n,k)$ . For every fixed $l$ , $v_l(n) \to \infty$ as $n \to \infty$

[ErSe67] Erdős, P. and Selfridge, J. L., Some problems on the prime factors of consecutive integers. Illinois J. Math. (1967), 428--430.

FormalConjectures/ErdosProblems/889.leanErdos889.erdos_889.variants.general1 lineExact file

1∀ (l : ℕ), Filter.Tendsto (Erdos889.v_l l) Filter.atTop (nhds ⊤)

OpenStatement only, no proof

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