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Full-Text Articles in Number Theory
Constructing Carmichael Numbers Through Improved Subset-Product Algorithms, W.R. Alford, Jon Grantham, Steven Hayman, Andrew Shallue
Constructing Carmichael Numbers Through Improved Subset-Product Algorithms, W.R. Alford, Jon Grantham, Steven Hayman, Andrew Shallue
Scholarship
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 .