2013/07/09 by W. R. Alford, Jon Grantham, Steven Hayman +1 · 1 citation
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #Advanced Mathematical Identities
paper · pdf · doi:10.1090/s0025-5718-2013-02737-8
openalex publication_date 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Λ.