Prime Numbers: A Computational Perspective

  title={Prime Numbers: A Computational Perspective},
  author={Richard E. Crandall and Carl Pomerance},
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… Expand
Survey on Prime Numbers
Primes are the building blocks of integer universe. Prime numbers plays a major role in number theory. This paper is a detailed survey on prime numbers.This describes different types of primes andExpand
Recent Breakthrough in Primality Testing
Prime numbers are rather old objects in mathematics, however, they did not loose their fascination and importance. Invented by the ancient Greek in an alogy to theindivisible atoms in physics, primesExpand
Primality Testing and Factorization Methods
Since the days of Euclid and Eratosthenes, mathematicians have taken a keen interest in finding the nontrivial factors of integers, as well as in finding prime numbers, which have no such factors.Expand
Factoring integers
The theory of numbers is primarily concerned with the properties of the natural numbers 1,2,3,. . . . The fundamental theorem of arithmetic states that each natural number > 1 can be expressedExpand
A collection of patterns for prime generation
This paper can be used for educational purposes, allowing students to become acquainted with the Mathematics and Algorithmics regarding the search of primes, as well as with the notion and use of patterns. Expand
Smooth numbers: computational number theory and beyond
The analysis of many number theoretic algorithms turns on the role played by integers which have only small prime factors; such integers are known as “smooth numbers”. To be able to determine whichExpand
Prime numbers are central to modern discrete mathematics. It is thus natural to ask the question, given a natural number, of whether it is prime or not. In fact, since there is no formula for the nExpand
The Lucas-Pratt primality tree
  • J. Bayless
  • Computer Science, Mathematics
  • Math. Comput.
  • 2008
It is shown that for all constants C ∈ R, the number of modular multiplications necessary to obtain this certificate is greater than Clog p for a set of primes p with relative asymptotic density 1. Expand
Phillip Mates 1 Problem Summary & Motivation
Primes are used pervasively throughout modern society. E-commerce, privacy, and psuedorandom number generators all make heavy use of primes. There currently exist many different primality tests, eachExpand
  • Aaron Ekstrom
  • Mathematics
  • Journal of the Australian Mathematical Society
  • 2012
Abstract In 1987, Gordon gave an integer primality condition similar to the familiar test based on Fermat’s little theorem, but based instead on the arithmetic of elliptic curves with complexExpand


An Introduction to the Theory of Numbers
This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,Expand
An introduction to the theory of numbers
Divisibility congruence quadratic reciprocity and quadratic forms some functions of number theory some diophantine equations Farey fractions and irrational numbers simple continued fractions primesExpand