A lower bound for the least prime in an arithmetic progression

Junxian Li, Kyle Pratt, George Shakan

Fix $k$ a positive integer, and let $\ell$ be coprime to $k$. Let $p(k,\ell )$ denote the smallest prime equivalent to $\ell (\mathrm{mod}k)$, and set $P(k)$ to be the maximum of all the $…