Erdős problem 386

There is a $k$ , such that $2 \le k \le n - 2$ and $\binom{n}{k}$ can be the product of consecutive primes infinitely often?

Sources

The source's own material, retained exactly.

3 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

386.lean

Retained formal statement2 of 3

For all $2 \le k \le n - 2$ , can $\binom{n}{k}$ be the product of consecutive primes infinitely often?

FormalConjectures/ErdosProblems/386.leanErdos386.erdos_386.variants.forall1 lineExact file

1True ↔ ∀ k ≥ 2, ∃ᶠ (n : ℕ) in Filter.atTop, k ≤ n - 2 ∧ ∃ p q, n.choose k = ∏ i ∈ Finset.Ico p q, Nat.nth Nat.Prime i

OpenStatement only, no proof