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Prime Numbers

A Computational Perspective

Richard Crandall, Carl B. Pomerance (Autoren)

Buch | Hardcover

597 Seiten

2005 | 2nd ed. 2005
Springer-Verlag New York Inc.
978-0-387-25282-7 (ISBN)

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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. The 2nd edition adds new material on primality and algorithms and updates all the numerical records, such as the largest prime, etc. It has been revised throughout.

From the reviews of the first edition:

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

American Scientist

… Crandall and Pomerance have written a terrific book.

Bulletin of the AMS

Richard Crandall currently holds the title of Apple Distinguished Scientist, having previously been Apples Chief Cryptographer, the Chief Scientist at NeXT, Inc., and recipient of the Vollum Chair of Science at Reed College. His primary interest is interdisciplinary scientific computation, though he has authored numerous theoretical papers in quantum physics, biology, mathematics, and chemistry, as well as various patents across engineering fields. Carl Pomerance received his Ph.D. in mathematics from Harvard University in 1972. Currently he is a professor at Dartmouth College. A popular lecturer and winner of the Chauvenet and Conant Prizes for expository mathematical writing, Pomerance is well known for his research in computational number theory, his efforts having produced important algorithms now in wide use.

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.

Zusatzinfo	143 Illustrations, black and white; XV, 597 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-25282-7 / 0387252827
ISBN-13	978-0-387-25282-7 / 9780387252827
Zustand	Neuware