Building pseudoprimes with a large number of prime factors

  • D. Guillaume
  • F. Morain


We extend the method due originally to Löh and Niebuhr for the generation of Carmichael numbers with a large number of prime factors to other classes of pseudoprimes, such as Williams's pseudoprimes and elliptic pseudoprimes. We exhibit also some new Dickson pseudoprimes as well as superstrong Dickson pseudoprimes.


Carmichael numbers Pseudoprimes Lucas pseudoprimes Elliptic pseudoprimes Strong Dickson pseudoprimes 


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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • D. Guillaume
    • 1
  • F. Morain
    • 2
  1. 1.VélizyFrance
  2. 2.LIX, Laboratoire d'Informatique de l'Ecole Polytechnique Ecole PolytechniquePalaiseau CedexFrance

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