erdos_457

Specification

Is there some $\epsilon > 0$ such that there are infinitely many $n$ where all primes $p \le (2 + \epsilon) \log n$ divide $$ \prod_{1 \le i \le \log n} (n + i)? $$

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Lean 4 Statement

theorem erdos_457 : answer(sorry) ↔ ∃ ε > (0 : ℝ),
    { (n : ℕ) | ∀ (p : ℕ), p ≤ (2 + ε) * Real.log n → p.Prime →
      p ∣ ∏ i ∈ Finset.Icc 1 ⌊Real.log n⌋₊, (n + i) }.Infinite

ID: ErdosProblems__457__erdos_457

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