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Constructing Carmichael numbers through improved subset-product algorithms
Mathematics of Computation (2014)
  • W.R. Alford
  • Jon Grantham
  • Steven Hayman
  • Andrew Shallue
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 .
  • subset sum,
  • Carmichael numbers
Publication Date
Publisher Statement
First published in Mathematics of Computation, volume 83, published by the American Mathematical Society
Citation Information
W.R. Alford, Jon Grantham, Steven Hayman and Andrew Shallue. "Constructing Carmichael numbers through improved subset-product algorithms" Mathematics of Computation Vol. 83 Iss. 286 (2014) p. 899 - 915
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Creative Commons License
This work is licensed under a Creative Commons CC_BY-NC-ND International License.