The class number "h" of the cyclotomic field formula_2 is a product of two integers "h"1 and "h"2, called the first and second factors of the class number, where "h"2 is the class number of the maximal real subfield formula_1 of the "p"-th cyclotomic field. The first factor "h"1 is well understood and can be computed easily in terms of Bernoulli numbers, and is usually rather large. The second factor "h"2 is not well understood and is hard to compute explicitly, and in the cases when it has been computed it is usually small.