Erdős problem 680 · problems.science

Is it true that, for all sufficiently large $n$ , there exists some $k$ such that $p(n+k)>k^2+1,$ where $p(m)$ denotes the least prime factor of $m$ ?

Sources

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

2 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

680.lean

Retained formal statement2 of 2

Can one prove this is false if we replace $k^2+1$ by $e^{(1+\epsilon)\sqrt{k}}+C_\epsilon$ , for all $\epsilon>0$ , where $C_\epsilon>0$ is some constant?

FormalConjectures/ErdosProblems/680.leanErdos680.erdos_680.parts.ii1 lineExact file

1True ↔ ∀ ε > 0, ∃ C > 0, ¬∀ᶠ (n : ℕ) in Filter.atTop, ∃ k, k ≠ 0 ∧ ↑(n + k).minFac > Real.exp ((1 + ε) * √↑k) + C

OpenStatement only, no proof

Sources

Search problems.science