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Prime Numbers
A Computational Perspective
Buch von Carl B. Pomerance (u. a.)
Sprache: Englisch

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Beschreibung
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
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
Über den Autor

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.

Zusammenfassung

In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts, including the striking new "AKS" test for recognizing prime numbers. Other examples: new computational results on the Riemann hypothesis, a very new and superfast pure-binary algorithm for the greatest common divisor, and new forms of the fast Fourier transform. The authors also list many new computational records and survey new developments in the theory of prime numbers, including the proof that there are arbitrarily long arithmetic progressions of primes and the proof that 8 and 9 are the only consecutive powers. Numerous exercises have also been added.

About the first edition:

"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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2005
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xv
597 S.
143 s/w Illustr.
ISBN-13: 9780387252827
ISBN-10: 0387252827
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Pomerance, Carl B.
Crandall, Richard
Auflage: 2nd ed. 2005
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Maße: 241 x 160 x 39 mm
Von/Mit: Carl B. Pomerance (u. a.)
Erscheinungsdatum: 04.08.2005
Gewicht: 1,08 kg
Artikel-ID: 102300150
Über den Autor

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.

Zusammenfassung

In the new edition of this highly successful book, Richard Crandall and Carl Pomerance have provided updated material on theoretical, computational, and algorithmic fronts, including the striking new "AKS" test for recognizing prime numbers. Other examples: new computational results on the Riemann hypothesis, a very new and superfast pure-binary algorithm for the greatest common divisor, and new forms of the fast Fourier transform. The authors also list many new computational records and survey new developments in the theory of prime numbers, including the proof that there are arbitrarily long arithmetic progressions of primes and the proof that 8 and 9 are the only consecutive powers. Numerous exercises have also been added.

About the first edition:

"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

Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2005
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Inhalt: xv
597 S.
143 s/w Illustr.
ISBN-13: 9780387252827
ISBN-10: 0387252827
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Pomerance, Carl B.
Crandall, Richard
Auflage: 2nd ed. 2005
Hersteller: Springer US
Springer New York
Springer US, New York, N.Y.
Maße: 241 x 160 x 39 mm
Von/Mit: Carl B. Pomerance (u. a.)
Erscheinungsdatum: 04.08.2005
Gewicht: 1,08 kg
Artikel-ID: 102300150
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