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Primes!

  • Richard Crandall
  • Carl Pomerance

Abstract

Prime numbers belong to an exclusive world of intellectual conceptions. We speak of those marvelous notions that enjoy simple, elegant description, yet lead to extreme—one might say unthinkable—complexity in the details. The basic notion of primality can be accessible to a child, yet no human mind harbors anything like a complete picture. In modern times, while theoreticians continue to grapple with the profundity of the prime numbers, vast toil and resources have been directed toward the computational aspect, the task of finding, characterizing, and applying the primes in other domains. It is this computational aspect on which we concentrate in the ensuing chapters. But we shall often digress into the theoretical domain in order to illuminate, justify, and underscore the practical import of the computational algorithms.

Keywords

Arithmetic Progression Riemann Zeta Function Riemann Hypothesis Decimal Digit Dirichlet Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, New York, Inc. 2001

Authors and Affiliations

  • Richard Crandall
    • 1
  • Carl Pomerance
    • 2
  1. 1.Center for Advanced ComputationPortlandUSA
  2. 2.Department of MathematicsDartmouth UniversityHanoverUSA

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