Fermat numbers, Wieferich and Wilson primes: computations and generalizations (Q2764231)

The paper is a survey of classical and recent computational results on several interrelated topics, dealing with properties (primality and factorization mainly) of some families of large integers.NEWLINENEWLINENEWLINEIn the first section the paper introduces the topics to be dealt with in the following. As a starting point the author considers the numbers \(2^n\) and \(n!\) and their (more interesting) neighbors \(2^n\pm 1\) and \(n!\pm 1\), as well as the classical arithmetical theorems of Fermat and Wilson.NEWLINENEWLINENEWLINEThen he chooses the following six topics, which are discussed separately in the following sections (sections 2 to 7): Fermat numbers, Generalized Fermat numbers, The search for Wieferich primes, Fermat quotients for composite moduli, The search for Wilson primes, Wilson quotients for composite moduli. NEWLINENEWLINENEWLINEThe paper presents the state of the art (up to 2001) of each one of these topics, its interrelations and the main issues of the ongoing computational research on them.NEWLINENEWLINEFor the entire collection see [Zbl 0976.00054].