Erdős problem 457 · problems.science

Is there some $\epsilon > 0$ such that there are infinitely many $n$ where all primes $p \le (2 + \epsilon) \log n$ divide $\prod_{1 \le i \le \log n} (n + i)?$

Sources

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

3 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

457.lean

Retained formal statement2 of 3

Taking $n$ to be the product of primes between $\log n$ and $(2 + o(1)) \log n$ gives an example where $q(n, \log n) \ge (2 + o(1)) \log n.$ Can one prove that $q(n, \log n) < (1 - \epsilon) (\log n)^2$ for all large $n$ and some $\epsilon > 0$ ?

FormalConjectures/ErdosProblems/457.leanErdos457.erdos_457.variants.one_sub1 lineExact file

1sorry ↔ ∃ ε > 0, ∀ᶠ (n : ℕ) in Filter.atTop, ↑(Erdos457.q n (Real.log ↑n)) < (1 - ε) * Real.log ↑n ^ 2

OpenStatement only, no proof

Sources

Search problems.science