Advertisement

Six proofs of the infinity of primes

  • Martin Aigner
  • Günter M. Ziegler

Abstract

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.

Keywords

Natural Number Prime Divisor Arithmetic Progression Fermat Number Product PIP2 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations