Abstract

Let $p\left(n\right)$ denote the smallest prime divisor of the integer $n$. Define the function $g\left(k\right)$ to be the smallest integer $>k+1$ such that $p\left(\left(\genfrac{}{}{0.0pt}{}{g\left(k\right)}{k}\right)\right)>k$. We present a new algorithm to compute the value of $g\left(k\right)$, and use it to both verify previous work and compute new values of $g\left(k\right)$, with our current limit being

We prove that our algorithm runs in time sublinear in $g\left(k\right)$, and under the assumption of a reasonable heuristic, its running time is

Keywords

Mathematical Subject Classification 2010

Supplementary material

Algorithm and estimates for the Erdos--Selfridge function

Milestones

Authors