Prime Numbers : A Computational Perspective

In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts, including the striking new "AKS" test for recognizing prime numbers. Other examples: new computational results on the Riemann hypothesis, a very new and superfast pure-binary algorithm for the greatest common divisor, and new forms of the fast Fourier transform. The authors also list many new computational records and survey new developments in the theory of prime numbers, including the proof that there are arbitrarily long arithmetic progressions of primes and the proof that 8 and 9 are the only consecutive powers. Numerous exercises have also been added.

About the first edition:

"Its rare to say this of a math book, but open Prime Numbers to a random page and its hard to put down. Crandall and Pomerance have written a terrific book."

- Bulletin of the AMS