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26 April 2024

» arxiv » 1203.6664

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Constructing Carmichael numbers through improved subset-product algorithms
W.R. Alford ; Jon Grantham ; Steven Hayman ; Andrew Shallue ;
Date:	29 Mar 2012
Abstract:	We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with k prime factors for every k between 3 and 19,565,220. These computations are the product of implementations of two new algorithms for the subset product problem that exploit the non-uniform distribution of primes p with the property that p-1 divides a highly composite Lambda.
Source:	arXiv, 1203.6664
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