R. Crandall And C. Pomerance. Prime Numbers: a Computational Approach

Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added.

In this volume we have endeavored to provide a middle ground-hopefully even a bridge-between "theory" and "experiment" in the matter of prime numbers. Of course, we speak of number theory and computer experiment. There are great books on the abstract properties of prime numbers. Each of us working in the field enjoys his or her favorite classics.