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Building Carmichael numbers with a large number of prime factors and generalization to other numbers

D. Guillaume François Morain 1
1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : We extend the method of Loh and Niebuhr for the generation of Carmichael numbers with a large number of prime factors to other classes of pseudoprimes. In particular, we exhibit the first known strong Fibonacci pseudoprimes. The method can be viewed as a simplified version, yet practical, of the method used by Alford, Granville and Pomerance to prove that there is an infinite number of Carmichael numbers.
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https://hal.inria.fr/inria-00076980
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Submitted on : Monday, May 29, 2006 - 11:45:52 AM
Last modification on : Friday, February 4, 2022 - 3:07:43 AM
Long-term archiving on: : Friday, May 13, 2011 - 10:20:01 PM

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  • HAL Id : inria-00076980, version 1

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D. Guillaume, François Morain. Building Carmichael numbers with a large number of prime factors and generalization to other numbers. [Research Report] RR-1741, INRIA. 1992. ⟨inria-00076980⟩

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