Hans Riesel

Prime Numbers and Computer Methods for Factorization (eBook, PDF)

• Format: PDF

Produktbeschreibung

Published in the mid 1980s, the highly successful first edition of this title investigated the mathematical underpinnings of computer encryption, a discipline drawing heavily on the factorization of large numbers into primes. The book served a broad audience of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination, treating four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes, and the factorization of large numbers.

The second edition of the work, released in the mid 1990s, expanded significantly upon the original book, including important advances in computational prime number theory and factorization, as well as revised and updated tables. With explicit algorithms and computer programs, the author illustrated applications while attempting to discuss many classically important results along with more modern discoveries.

Although it has been over a decade since the publication of this second edition, the theory it contained remains still highly relevant, and the particular cryptosystem it addressed (RSA public-key) is ubiquitous. Therefore, in addition to providing a historical perspective on many of the issues in modern prime number theory and data encryption, this soft cover version-which reproduces the second edition exactly as it originally appeared-offers affordable access to a great deal of valuable information. Highly readable for a wide variety of mathematicians, students of applied number theory, and others, this modern classic will be of interest to anyone involved in the study of number theory and cryptography.

Reviews:

Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition... All in all, this handy volumecontinues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science. -Zentralblatt MATH

The book...is an enthusiastic introduction to some of the ideas concerned with primes and factorization. It should be of interest to anyone who would like to learn about the use of computers in number theory. -Mathematical Reviews

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Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 464
• Erscheinungstermin: 23. November 2011
• Englisch
• ISBN-13: 9780817682989
• Artikelnr.: 37364455

Inhaltsangabe

Preface.-The Number of Primes Below a Given Limit.-The Primes Viewed at Large.-Subtleties in the Distribution of Primes.-The Recognition of Primes.-Classical Methods of Factorization.-Modern Factorization Methods.-Prime Numbers and Cryptography.-Appendix 1. Basic Concepts in Higher Algebra.-Appendix 2. Basic concepts in Higher Arithmetic.-Appendix 3. Quadratic Residues.-Appendix 4. The Arithmetic of Quadratic Fields.-Appendix 5. Higher Algebraic Number Fields.-Appendix 6. Algebraic Factors.-Appendix 7. Elliptic Curves.-Appendix 8. Continued Fractions.-Appendix 9. Multiple-Precision Arithmetic.-Appendix 10. Fast Multiplication of Large Integers.-Appendix 11. The Stieltjes Integral.-Tables.-List of Textbooks.-Index.

Rezensionen

Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition... All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science. -Zentralblatt MATH

The book...is an enthusiastic introduction to some of the ideas concerned with primes and factorization. It should be of interest to anyone who would like to learn about the use of computers in number theory. -Mathematical Reviews

Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition... All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science. -Zentralblatt MATH

The book...is an enthusiastic introduction to some of the ideas concerned with primes and factorization. It should be of interest to anyone who would like to learn about the use of computers in number theory. -Mathematical Reviews

"Here is an outstanding technical monograph on recursive number theory and its numerous automated techniques. It successfully passes a critical milestone not allowed to many books, viz., a second edition. Many good things have happened to computational number theory during the ten years since the first edition appeared and the author includes their highlights in great depth. Several major sections have been rewritten and totally new sections have been added. The new material includes advances on applications of the elliptic curve method, uses of the number field sieve, and two new appendices on the basics of higher algebraic number fields and elliptic curves. Further, the table of prime factors of Fermat numbers has been significantly up-dated. ...Several other tables have been added so as to provide data to look for large prime factors of certain 'generalized' Fermat numbers, while several other tables on special numbers were simply deleted in the second edition. Still one can make several perplexing assertions or challenges: (1) prove that F\sb 5, F\sb 6, F\sb 7, F\sb 8 are the only four consecutive Fermat numbers which are bi-composite; (2) Show that F\sb{14} is bi- composite. (This accounts for the difficulty in finding a prime factor for it.) (3) What is the smallest Fermat quadri-composite?; and (4) Does there exist a Fermat number with an arbitrarily prescribed number of prime factors? All in all, this handy volume continues to be an attractive combination of number-theoretic precision, practicality, and theory with a rich blend of computer science." -Zentralblatt Math