Six proofs of the infinity of primes

  • Martin Aigner
  • Günter M. Ziegler


It is only natural that we start these notes with probably the oldest Book Proof, usually attributed to Euclid (Elements IX, 20). It shows that the sequence of primes does not end.


Natural Number Prime Divisor Arithmetic Progression Fermat Number Product PIP2 
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  1. [1]
    B. Artmann: Euclid — The Creation of Mathematics, Springer-Verlag, New York 1999.MATHCrossRefGoogle Scholar
  2. [2]
    P. Erdős: Über die Reihe Σ 1/P, Mathematica, Zutphen B 7 (1938), 1–2.Google Scholar
  3. [3]
    L. Euler: Introductio in Analysin Infinitorum, Tomus Primus, Lausanne 1748; Opera Omnia, Ser. 1, Vol. 8.Google Scholar
  4. [4]
    H. FÜrstenberg: On the infinitude of primes, Amer. Math. Monthly 62 (1955), 353.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, MA 6-2Technische Universität BerlinBerlinGermany

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