Constructing Carmichael numbers through improved subset-product algorithms

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 prob- lem that exploit the non-uniform distribution of primes p with the property that p 1 divides a highly composite .

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