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Erdős problem 891

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Let 2=p1<p2<⋯2=p_1 < p_2 < \cdots be the primes and k≥2k\geq 2. Is it true that, for all sufficiently large nn, there must exist an integer in [n,n+p1⋯pk)[n,n+p_1\cdots p_k) with >k>k many prime factors?

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4 retained statements36c6d0fef71a

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FormalConjectures/ErdosProblems/

891.lean

Retained formal statement2 of 4

This is unknown even for k=2k=2 - that is, is it true that in every interval of 66 (sufficiently large) consecutive integers there must exist one with at least 33 prime factors?

FormalConjectures/ErdosProblems/891.leanErdos891.erdos_891.variants.case_k_21 lineExact file
True ↔ ∀ᶠ (n : ℕ) in Filter.atTop, ∃ m ∈ Finset.Ico n (n + 6), 3 ≤ ArithmeticFunction.cardDistinctFactors m
OpenStatement only, no proof