Erdős problem 649

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

The source's own material, retained exactly.

6 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

649.lean

Retained formal statement6 of 6

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

Source providers

Erdős Problems1
locator only
Formal Conjectures6
statement retained
VibeMathed0
not observed here
PLBY Lean proofs1
no statement retained
Jayyhk Erdős Lean1
no statement retained
William Blair Lean proofs0
not observed here
Erdős AI contributions wiki1
no statement retained
GPT-Erdős0
not observed here

Referenced paths

FormalConjectures/
- ErdosProblems/
  - 649.lean6