Erdős problem 649 · problems.science

Let $P(m)$ denote the greatest prime factor of $m$ . Is it true that, for any two primes $p,q$ , there exists some integer $n$ such that $P(n)=p$ and $P(n+1)=q$ ?

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FormalConjectures/ErdosProblems/

649.lean

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Tong asks whether, for any given odd prime $q$ , there are infinitely many primes $p$ such that there is no integer $n$ with $P(n)=p$ and $P(n+1)=q$ .

FormalConjectures/ErdosProblems/649.leanErdos649.erdos_649.variants.tong_question1 lineExact file

1True ↔ ∀ (q : ℕ), Nat.Prime q → Odd q → {p | Nat.Prime p ∧ ¬∃ n, n.maxPrimeFac = p ∧ (n + 1).maxPrimeFac = q}.Infinite

OpenStatement only, no proof

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