#### Abstract

We have constructed a Carmichael number with 10,333,229,505 prime factors, and have also constructed Carmichael numbers with prime factors for every 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 with the property that divides a highly composite .

#### 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.

http://digitalcommons.iwu.edu/math_scholarship/1

## Comments

First published in Mathematics of Computation, volume 83, published by the American Mathematical Society