Computers as Novel Mathematical Reality. VI. Fermat numbers and their relatives

Abstract

In this part, which constitutes a pendent to the part dedicated to Mersenne numbers, I continue to discuss the fantastic contributions towards the solution o classical problems of number theory achieved over the last decades with the use of computers. Specifically, I address primality testing, factorisations and the search of prime divisors of the numbers of certain special form, primarily Fermat numbers, their friends and relations, such as generalised Fermat numbers, Proth numbers, and the like. Furthermore, we discuss the role of Fermat primes and Pierpoint primes in cyclotomy.