The Ubiquity of Prime Numbers

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

Chapter Chapter 8 in Prime Numbers, 2001, pp 353-406 from Springer

Abstract: Abstract It is often remarked that prime numbers finally found a legitimate practical application in the domain of cryptography. The cryptographic relevance is not disputed, but there are many other applications of the majestic primes. Some applications are industrial—such as applications in numerical analysis, applied mathematics, and other applied sciences—while some are of the “conceptual feedback” variety, in which primes and their surrounding concepts are used in theoretical work outside of, say, pure number theory. In this lucrative research mode, primes are used within algorithms that might appear a priori independent of primes, and so on. It seems fair to regard the prime number concept as ubiquitous, since the primes appear in so very many disparate domains of thought.

Keywords: Prime Number; Elliptic Curf; Discrete Logarithm; Riemann Hypothesis; Elliptic Curve Cryptography (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4684-9316-0_8

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