Infinitude of regular primes

Determine whether there are infinitely many regular primes, i.e., primes p for which p does not divide the class number of the p-th cyclotomic field (equivalently, p does not divide any of the numerators of the Bernoulli numbers B2, B4, ..., Bp−3).

Background

In discussing Kummer’s approach to Fermat’s Last Theorem via unique factorization in cyclotomic fields, the authors note that his method proves the theorem for the so-called regular primes. The unresolved question is whether there are infinitely many such primes.

This problem arises naturally from algebraic number theory and the paper of cyclotomic fields, and it remains notorious despite partial results and extensive computation.