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

Retained formal statement3 of 6

Problem 6 in the 12th Romanian Master of Mathematics Competitions in 2020 was to prove that there exist infinitely many odd primes $p$ such that, for every $n$ , $P(n)P(n+1)\neq 2p$ .

FormalConjectures/ErdosProblems/649.leanErdos649.erdos_649.variants.rmm_20201 lineExact file

1{p | Nat.Prime p ∧ Odd p ∧ ∀ (n : ℕ), n.maxPrimeFac * (n + 1).maxPrimeFac ≠ 2 * p}.Infinite

TextbookStatement only, no proof

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