FormalConjectures.ErdosProblems.«383»

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import FormalConjecturesUtil

Erdős Problem 383

Reference: erdosproblems.com/383


namespace Erdos383

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 $p$?

@[category research open, AMS 11]
theorem declaration uses 'sorry'erdos_383 : answer(sorry) ↔
    ∀ k, {p : ℕ | p.Prime ∧ Nat.maxPrimeFac (∏ i ∈ Finset.Icc 0 k, (p ^ 2 + i)) = p}.Infinite := by⊢ True ↔ ∀ (k : ℕ), {p | Nat.Prime p ∧ (∏ i ∈ Finset.Icc 0 k, (p ^ 2 + i)).maxPrimeFac = p}.Infinite
  sorryAll goals completed! 🐙


end Erdos383