Prime Numbers: A Computational Perspective - Hardcover

Richard Crandall

Hardcover

ISBN 10: 0387947779 ISBN 13: 9780387947778

Publisher: Springer, 2002

Synopsis

Prime numbers beckon to the beginner, the basic notion of primality being accessible to a child. Yet, some of the simplest questions about primes have stumped humankind for millennia. In this book, the authors concentrate on the computational aspects of prime numbers, such as recognizing primes and discovering the fundamental prime factors of a given number. Over 100 explicit algorithms cast in detailed pseudocode are included in the book. Applications and theoretical digressions serve to illuminate, justify, and underscore the practical power of these algorithms. This book can be read on several levels. For those wanting a taste of the lore of prime numbers and the principal methods to deal with them, the book provides a friendly introduction. For those wanting to delve deeper into the essential details of the most up-to-date methods for prime number computations, the book has such details and many references to the huge literature on the subject. Students can test their understanding with interesting exercises, including some entertaining, nonstandard ones. And for those wishing to start or enrich a research program in computational prime number theory, the many unsolved problems in the text, and research problems in the exercises, provide rich ground for further work.

About this title

From the Back Cover

Prime numbers beckon to the beginner, as the basic notion of primality is accessible even to children. Yet, some of the simplest questions about primes have confounded humankind for millennia. In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts. New results discussed include the AKS test for recognizing primes, computational evidence for the Riemann hypothesis, a fast binary algorithm for the greatest common divisor, nonuniform fast Fourier transforms, and more. The authors also list new computational records and survey new developments in the theory of prime numbers, including the magnificent proof that there are arbitrarily long arithmetic progressions of primes, and the final resolution of the Catalan problem. Numerous exercises have been added.

Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apple's Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. Though he publishes in quantum physics, biology, mathematics, and chemistry, and holds various engineering patents, his primary interest is interdisciplinary scientific computation. Carl Pomerance is the recipient of the Chauvenet and Conant Prizes for expository mathematical writing. He is currently a mathematics professor at Dartmouth College, having previously been at the University of Georgia and Bell Labs. A popular lecturer, he is well known for his research in computational number theory, his efforts having produced important algorithms now in use.

From the reviews of the first edition:

"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."

^ L'Enseignement Mathématique

"...Prime Numbers is a welcome addition to the literature of number theory---comprehensive, up-to-date and written with style."

- American Scientist

"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."

- Bulletin of the AMS

About the Author

Rick Crandall, Ph.D., author of "Marketing Your Services: For People Who Hate to Sell", is a professional writer, consultant, and entrepreneur. He has written and lectured for "Inc." magazine and the American Marketing Association.

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 0387947779
• ISBN 13: 9780387947778
• Binding: Hardcover
• Edition number: 2
• Number of pages: 568