Publication Date
1-1-2014
Abstract
style="color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px;">We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with style="color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px;"> prime factors for every style="color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px;"> 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 style="color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px;">with the property that style="color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px;"> divides a highly composite style="color: rgb(51, 51, 51); font-family: "Helvetica Neue", Helvetica, Arial, sans-serif; font-size: 14px;">.
Disciplines
Mathematics | Number Theory | Theory and Algorithms
Recommended Citation
Alford, W.R.; Grantham, Jon; Hayman, Steven; and Shallue, Andrew, "Constructing Carmichael numbers through improved subset-product algorithms" (2014). Scholarship. 1.
https://digitalcommons.iwu.edu/math_scholarship/1
Comments
First published in Mathematics of Computation, volume 83, published by the American Mathematical Society