Regular prime

Summary

An odd prime number $p$ is regular if it does not divide the class number of the cyclotomic field $\Q(\zeta_p)$. Kummer introduced regular primes and proved Fermat's Last Theorem for every regular prime exponent. By Kummer's criterion, $p$ is regular exactly when $p$ divides none of the numerators of the Bernoulli numbers $B_2, B_4, \ldots, B_{p-3}$. The smallest irregular prime is $37$.