Let $r$ be a uniformly random integer between $1$ and $N$, for some large enough $N$ (i.e., I'm only interested in the asymptotics).

  • What is the expected largest prime factor of $r$? Is there a good upper bound on this?

  • Let $t < N$ be such that $\Pr\Big[r $ has no prime factor > $t\Big] = \Omega(1/\log^c(N))$ for some constant $c > 0$. How small can we make $t$? Is $t = \operatorname{Li}_2(N)$ achievable?


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.