How Many Prime Numbers Are There?

  • Paulo Ribenboim


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.


Prime Number Prime Ideal Fundamental Theorem Prime Divisor Arithmetic Progression 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Paulo Ribenboim
    • 1
  1. 1.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada

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