This text is not a theoretical mathematics book, but an advanced exposition algorithms for prime number computations -- some relatively modern (circa 2000). The text is clearly written and organized. It may be successfully used by a range of readers from those wishing to to understand the way algorithms work at an intuitive level to readers simply wishing to use it in a cookbook fashion to quickly implement various algorithms. While this is not a theoretical text, the authors have still taken pains to be very careful mathematically in the presentation of the material. At the same time they present significant quantities of "meta-mathematical" material designed to impart an intuitive grasp of the subject as well. The examples are topical and reinforce an understanding of the material. The exercises are numerous and range from simple problems to research level material suitable for a PhD thesis. This is a must own for any computational number theorist or anyone interested in prime number computations.
