Prime Numbers and Computer Methods for Factorization (Progress in Mathematics (Birkhauser Boston)
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In this book the author treats four fundamental and apparently simple problems. They are: the number of primes below a given limit, the ap­ proximate number of primes, the recognition of prime numbers and the factorization of large numbers. A chapter on the details of the distribution of the primes is included as well as a short description of a recent applica­ tion of prime numbers, the so-called RSA public-key cryptosystem. The author is also giving explicit algorithms and computer programs. Whilst not claiming completeness, the author has tried to give all important results known, including the latest discoveries. The use of computers has in this area promoted a development which has enormously enlarged the wealth of results known and that has made many older works and tables obsolete. As is often the case in number theory, the problems posed are easy to understand but the solutions are theoretically advanced. Since this text is aimed at the mathematically inclined layman, as well as at the more advanced student, not all of the proofs of the results given in this book are shown. Bibliographical references in these cases serve those readers who wish to probe deeper. References to recent original works are also given for those who wish to pursue some topic further. Since number theory is seldom taught in basic mathematics courses, the author has appended six sections containing all the algebra and number theory required for the main body of the book. eBook.

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Prime Numbers and Computer Methods for Factorization: In this book the author treats four fundamental and apparently simple problems. They are: the number of primes below a given limit, the ap- proximate number of primes, the recognition of prime numbers and the factorization of large numbers. A chapter on the details of the distribution of the primes is included as well as a short description of a recent applica- tion of prime numbers, the so-called RSA public-key cryptosystem. The author is also giving explicit algorithms and computer programs. Whilst not claiming completeness, the author has tried to give all important results known, including the latest discoveries. The use of computers has in this area promoted a development which has enormously enlarged the wealth of results known and that has made many older works and tables obsolete. As is often the case in number theory, the problems posed are easy to understand but the solutions are theoretically advanced. Since this text is aimed at the mathematically inclined layman, as well as at the more advanced student, not all of the proofs of the results given in this book are shown. Bibliographical references in these cases serve those readers who wish to probe deeper. References to recent original works are also given for those who wish to pursue some topic further. Since number theory is seldom taught in basic mathematics courses, the author has appended six sections containing all the algebra and number theory required for the main body of the book. Englisch, Ebook.

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This edition has been updated to include advances in computational prime number theory and in factorization, as well as re-computed and enlarged tables, accompanied by new tables reflecting research by both the author and his co-workers, and by independent researchers. The book treats four fundamental problems: the number of primes below a given limit; the approximation of primes; the recognition of primes; and the factorization of large numbers. The author provides explicit algorithms and computer programs, which are written in PASCAL in order to allow the reader to translate the programs into the language of their own computers. Kindle Edition, Edition: 1, Format: Kindle eBook, Label: Birkhauser, Birkhauser, Product group: eBooks, Published: 1987-01-01, Release date: 1987-01-01, Studio: Birkhauser, Sales rank: 4511916.

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