Prime Numbers: A Computational Perspective, Second Edition

Richard E. Crandall and Carl Pomerance, 2005, Springer Science+Business Media, 597 pp., hardcover

ISBN: 0387252827

The text provides theoretical explanations for the practical power of computational algorithms, along with detailed pseudocode and exercises designed to keep students engaged and interested. It is a reference for professionals and students interested in prime numbers and encryption, cryptography, factoring algorithms, elliptic curve arithmetic, and many more computational issues related to primes and factoring.

Contents
Primes! | Number-Theoretical Tools | Recognizing Primes and Composites | Primality Proving | Exponential Factoring Algorithms | Subexponential Factoring Algorithms | Elliptic Curve Arithmetic | The Ubiquity of Prime Numbers | Fast Algorithms for Large-Integer Arithmetic | Appendix: Book Pseudocode

This book is available in the Wolfram Research bookstore.