Primes and Programming [Paperback]

In this introductory book Dr Giblin describes methods that have been developed for testing the primality of numbers, provides Pascal programs for their implementation, and gives applications to coding.Primality has recently become of commercial importance because it is related to the security of codes. This introductory book describes some of the more elementary methods of factorization and primality testing that do not require detailed knowledge of other areas of mathematics.Primality has recently become of commercial importance because it is related to the security of codes. This introductory book describes some of the more elementary methods of factorization and primality testing that do not require detailed knowledge of other areas of mathematics.Peter Giblin describes, in the context of an introduction to the theory of numbers, some of the more elementary methods for factorization and primality testing; that is, methods independent of a knowledge of other areas of mathematics. Indeed everything is developed from scratch so the mathematical prerequisites are minimal. An essential feature of the book is the large number of computer programs (written in Pascal) and a wealth of computational exercises and projects, in addition to more usual theory exercises. The theoretical development includes continued fractions and quadratic residues, directed always towards the two fundamental problems of primality testing and factorization. There is time, all the same, to include a number of topics and projects of a purely recreational nature.Preface; 1. The fundamental theorem, GCDs and LCMs; 2. Listing primes; 3. Congruences; 4. Powers and pseudoprimes; 5. Miller's test and strong pseudoprimes; 6. Euler's theorem, orders and primality testing; 7. Cryptography; 8. Primitive roots; 9. The number of divisors d and the sum of divisors; 10. Continued fractions and factoring; 11. Quadratic residues; References; Index. An interesting, sophisticated introduction to number theory..lÃj