On the Combined Fermat/Lucas Probable Prime Test⋆

  • Siguna Müller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1746)


Based on the well-known Baillie/Wagstaff suggestion [2] we introduce a rapid pseudoprimality test with high confidence. The test is extremely fast and only requires evaluation of power polynomials and the Lucas V -sequence. This is in contrast to the original version, where usually the more cumbersome evaluation of the Lucas U-sequence is required as well. We analyze the underlying properties of the proposed test and give a characterization of the pseudoprimes. Software and hardware evaluation methods for both modular exponentiation and evaluation of recursion sequences are widely employed and very efficient. Therefore the test can be run at low cost for varieties of different bases/parameters. The number of those that pass the test are of great interest. We exhibit the exact number of these “liars”.


Prime Divisor Prime Basis Combine Test Modular Exponentiation Recurrence Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Siguna Müller
    • 1
  1. 1.Dept. of Math.University of KlagenfurtKlagenfurtEurope

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