Prime Numbers and Computer Methods for Factorization (Progress in Mathematics) (Hardcover)

~ (Author) "Consider the positive integers 1,2,3,4....." (more)
Key Phrases: primitive residue classes, admissible constellation, small quadratic residues, Carl Pomerance, New York, Daniel Shanks (more...)

Editorial Reviews

Review

"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

Product Description

In the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called RSA public-key cryptosystem. A major component of this system is the factorization of large numbers into their primes. Thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics.

Hans Riesel’s highly successful first edition of this book has now been enlarged and updated with the goal of satisfying the needs of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination. It includes important advances in computational prime number theory and in factorization as well as re-computed and enlarged tables, accompanied by new tables reflecting current research by both the author and his coworkers and by independent researchers.

The book treats 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 author provides explicit algorithms and computer programs, and has attempted to discuss as many of the classically important results as possible, as well as the most recent discoveries. The programs include are written in PASCAL to allow readers to translate the programs into the language of their own computers.

The independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography.

Product Details

• Hardcover: 464 pages
• Publisher: Birkhäuser Boston; 2nd edition (October 1, 1994)
• Language: English
• ISBN-10: 0817637435
• ISBN-13: 978-0817637439
• Product Dimensions: 9.3 x 6.4 x 1.4 inches
• Shipping Weight: 1.8 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #1,243,457 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

10 of 10 people found the following review helpful:

5.0 out of 5 stars Excellent book, March 24, 2000

By	Cheslaw Oleinik (Kishinev, Moldova) - See all my reviews

Excellent book published on primes, primality proving and numbers factoring. The book are written for mathematicians not computer security professionals, have sections on public keys and Pascal code for various factorization methods. There are seven chapters and there are nine appendices. The book begins with a good introduction the concept of a prime number and the prime number theorem. The chapters deal with fundamental problems: The Number of Primes Below a Given Limit, Subtleties in the Distribution of Primes, The Recognition of Primes and Methods of Factorization.The factoring methods is broken into two chapters, one on classical method and one on modern methods. The seventh chapter is a short presentation on RSA cryptosystem. The second half of the book is split between the appendices and the tables. The tables are composed of primes, factors in many formats, quadratic residues and formulas for cyclotomic polynomials. There is also an appendix devoted to elliptic curves.

I will be pleased if in a next edition a diskette with the programs of examples is included.

1 of 1 people found the following review helpful:

5.0 out of 5 stars Yes, Excellent Book, December 16, 2001

By	Randy Given (Manchester, CT USA) - See all my reviews (TOP 500 REVIEWER)    (REAL NAME)

I think this is an excellent book as well. I bought it soon after it came out and read it. I was impressed. It has been impressive enough to stay on my bookshelf since the. Just today, I had to look up some information on factoring and remembered what a great book it is -- so I am leaving a review here. The only thing is that the code is in Pascal, which is not bad, but not like C++ or Java. Still, the book is detailed and informative.