Infinitude of non-Wieferich primes

A prime $p$ is non-Wieferich if there is an integer $N$ for which $N^{p-1}\not\equiv1\pmod{p^2}$. Infinitude conjecture for non-Wieferich primes. There exist infinitely many non-Wieferich primes. This is one of the two old prime-number conjectures identified in the paper as still open; the paper also discusses related finite multiple zeta values.