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 $P(n+1)=q$ ?

Sources

Browse retained paths and inspect the exact material available for this Problem.

6 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

649.lean

Retained formal statement2 of 6

In fact, the answer to this question as written is easily seen to be no, since there are no solutions to $2^k\equiv -1\pmod{7}$ , and hence this fails with $p=2$ and $q=7$ .

FormalConjectures/ErdosProblems/649.leanErdos649.erdos_649.variants.no_solution_two_seven1 lineExact file

1¬∃ n, n.maxPrimeFac = 2 ∧ (n + 1).maxPrimeFac = 7

TextbookStatement only, no proof

Sources

Search problems.science