In the middle of the last century, Kummer's studies on the famous Fermat conjecture led him to the question: when does a given prime p > 2 divide the class number of the p-th cyclotomic field? His conclusion was that this happens, if, and only if, p divides at least one of the Bernoulli numbers B2, B4,…, Bp_3. Such a prime is called irregular. Carlitz  has given the simplest proof of the fact that the number of irregular primes is infinite. However, it is not known whether there are infinitely many regular primes.