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erdos_383

Specification

Is it true that for every $k$ there are infinitely many primes $p$ such that the largest prime divisor of $$ \prod_{i = 0}^k (p ^ 2 + i) $$ is $p$?

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Lean 4 Statement 
theorem erdos_383 : answer(sorry) ↔
    ∀ k, {p : ℕ | p.Prime ∧ Nat.maxPrimeFac (∏ i ∈ Finset.Icc 0 k, (p ^ 2 + i)) = p}.Infinite
ID: ErdosProblems__383__erdos_383
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