Primes!

Richard Crandall () and Carl Pomerance ()
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Richard Crandall: Center for Advanced Computation
Carl Pomerance: Dartmouth University, Department of Mathematics

Chapter Chapter 1 in Prime Numbers, 2001, pp 1-76 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4684-9316-0_1

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