How Many Prime Numbers Are There?

Paulo Ribenboim
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Paulo Ribenboim: Queen’s University, Department of Mathematics and Statistics

Chapter 1 in The New Book of Prime Number Records, 1996, pp 3-18 from Springer

Abstract: Abstract The answer to the question of how many prime numbers exist is given by the fundamental theorem: There exist infinitely many prime numbers. I shall give several proofs of this theorem (plus three variants) by famous, but also by forgotten, mathematicians. Some proofs suggest interesting developments; other proofs are just clever or curious. There are of course more (...but not quite infinitely many) proofs of the existence of infinitely many primes.

Keywords: Prime Number; Prime Ideal; Fundamental Theorem; Prime Divisor; Arithmetic Progression (search for similar items in EconPapers)
Date: 1996
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DOI: 10.1007/978-1-4612-0759-7_2

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