Let $2=p_1 k$ many prime factors?

Erdős problem 891 · problems.science

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

Sources

Browse retained paths and inspect the exact material available for this Problem.

4 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

891.lean

Retained formal statement1 of 4

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

FormalConjectures/ErdosProblems/891.leanErdos891.erdos_8914 linesExact file

1True ↔2  ∀ k ≥ 2,3    ∀ᶠ (n : ℕ) in Filter.atTop,4      ∃ m ∈ Finset.Ico n (n + ∏ i ∈ Finset.range k, Nat.nth Nat.Prime i), k < ArithmeticFunction.cardDistinctFactors m

OpenStatement only, no proof

Sources

Search problems.science