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arXiv · 1203.6664

Constructing Carmichael numbers through improved subset-product algorithms

W. R. Alford·Jon Grantham·Steven Hayman·Andrew Shallue
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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.

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W. R. Alford, Jon Grantham, Steven Hayman, Andrew Shallue. 2012-03-29. Constructing Carmichael numbers through improved subset-product algorithms. https://arxiv.org/abs/1203.6664

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