Primality Proving

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

Chapter Chapter 4 in Prime Numbers, 2001, pp 159-190 from Springer

Abstract: Abstract In Chapter 3 we discussed probabilistic methods for quickly recognizing composite numbers. If a number is not declared composite by such a test, it is either prime, or we have been unlucky in our attempt to prove the number composite. Since we do not expect to witness inordinate strings of bad luck, after a while we become convinced that the number is prime. We do not, however, have a proof; rather, we have a conjecture substantiated by numerical experiments. This chapter is devoted to the topic of how one might actually prove that a number is prime.

Keywords: Prime Factor; Primitive Root; Modular Multiplication; Chinese Remainder Theorem; Fermat Number (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/978-1-4684-9316-0_4

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