erdos_891.variants.schinzel

Schinzel deduced from Pólya's theorem [Po18] (that the sequence of $k$-smooth integers has unbounded gaps) that this is true with $p_1\cdots p_k$ replaced by $p_1\cdots p_{k-1}p_{k+1}$.

theorem erdos_891.variants.schinzel :
    ∀ k ≥ 2, ∀ᶠ n in atTop,
      ∃ m ∈ Ico n (n + (∏ i ∈ range (k - 1), i.nth Nat.Prime) * k.nth Nat.Prime),
      k < ω m

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