Constructing Carmichael numbers through improved subset-product algorithms
Number Theory
2019-03-13 v2
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.
Keywords
Cite
@article{arxiv.1203.6664,
title = {Constructing Carmichael numbers through improved subset-product algorithms},
author = {W. R. Alford and Jon Grantham and Steven Hayman and Andrew Shallue},
journal= {arXiv preprint arXiv:1203.6664},
year = {2019}
}
Comments
Table 1 fixed; previously the last 30 digits and number of digits were calculated incorrectly