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erdos_386.variants_two

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Can $\binom{n}{2}$ be the product of consecutive primes infinitely often?

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Lean 4 Statement 
theorem erdos_386.variants_two :
    answer(sorry) ↔ ∃ᶠ n in .atTop,
      2 ≤ n - 2 ∧ ∃ p q : ℕ, n.choose 2 = ∏ i ∈ .Ico p q, nth Nat.Prime i
ID: ErdosProblems__386__erdos_386.variants_two
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