From the reviews‎:‎ MATHEMATICAL REVIEWS ‎"‎There are many books about the theory of prime numbers and a few about computations concerning primes‎.‎ This book bridges the gap between theoretical and computational aspects of prime numbers‎.‎ It considers such matters as how to recognize primes‎,‎ how to compute them‎,‎ how to count them‎,‎ and how to test conjectures about them‎?‎‎?‎The book is clearly written and is a pleasure to read‎.‎ It is largely self‎-contained‎.‎ A first course in number theory and some knowledge of computer algorithms should be sufficient background for reading it‎?‎‎?‎‎?‎Each chapter concludes with a long list of interesting exercises and research problems‎.‎‎"‎ BULLETIN OF THE AMS ‎"‎The book is an excellent resource for anyone who wants to understand these algorithms‎,‎ learn how to implement them‎,‎ and make them go fast‎.‎ It‎'‎s also a lot of fun to read‎!‎ It‎'‎s rare to say this of a math book‎,‎ but open Prime Numbers to a random page and it‎'‎s hard to put down‎.‎ Crandall and Pomerance have written a terrific book‎.‎‎"‎ AMERICAN SCIENTIST ‎"‎‎?‎‎?‎‎?‎a welcome addition to the literature of number theory ‎?‎‎?‎‎?‎ comprehensive‎,‎ up‎-to‎-date and written with style‎.‎ It will be useful to anyone interested in algorithms dealing with the arithmetic of the integers and related computational issues‎.‎‎"‎ SIAM REVIEW ‎"‎Overall‎,‎ this book by Crandall and Pomerance fills a unique niche a deserves a place on the bookshelf of anyone with more than a passing interest in prime numbers‎.‎ It would provide a gold mine of information and problems for a graduate class on computationl number theory‎.‎‎"‎ From the reviews of the second edition‎:‎ ‎"‎This book is a very successful attempt of the authors to describe thecurrent state‎-of‎-the‎-art of computational number theory ‎?‎‎?‎‎?‎ ‎.‎ One of the many attractive features of this book is the rich and beautiful set of exercises and research problems ‎?‎‎?‎‎?‎ ‎.‎ the authors have managed to lay down their broad and deep insight in primes into this book in a very lucid and vivid way‎.‎ ‎?‎‎?‎‎?‎ The book provides excellent material for graduate and undergraduate courses on computational theory‎.‎ Warmly recommended ‎?‎‎?‎‎?‎ ‎.‎‎"‎ ‎(‎H‎.‎J‎.‎J‎.‎ te Riele‎,‎ Nieuw Archief voor Wiskunde‎,‎ Vol‎.‎ 7 ‎(‎3‎)‎‎,‎ 2006‎)‎ ‎"‎An absolutely wonderful book‎!‎ Written in a readable and enthusiastic style the authors try to share the elegance of the prime numbers with the readers ‎?‎‎?‎‎?‎ ‎.‎ Weaving together a wealth of ideas and experience from theory and practice they enable the reader to have more than a glimpse into the current state of the knowledge ‎?‎‎?‎‎?‎ ‎.‎ any chapter or section can be singled out for high praise‎.‎ ‎?‎‎?‎‎?‎ Indeed it is destined to become a definitive text on ‎?‎‎?‎‎?‎ prime numbers and factoring‎.‎‎"‎ ‎(‎Peter Shiu‎,‎ Zentralblatt MATH‎,‎ Vol‎.‎ 1088 ‎(‎14‎)‎‎,‎ 2006‎)‎