Destined to become a definitive textbook conveying the most modern computational ideas about prime numbers and factoring, this book will stand as an excellent reference for this kind of computation, and thus be of interest to both educators and researchers. It is also a timely book, since primes and factoring have reached a certain vogue, partly because of cryptography. The final chapter focusses on "applications" of prime numbers, incorporating the mathematics of finance, via quasi-Monte Carlo theory. Historical comments are contained in every chapter.