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 .
Mathematics | Number Theory | Theory and Algorithms
Alford, W.R.; Grantham, Jon; Hayman, Steven; and Shallue, Andrew, "Constructing Carmichael numbers through improved subset-product algorithms" (2014). Scholarship. 1.