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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Constructing Carmichael numbers through improved subset-product algorithms
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by \fbox{W. R. } Alford, Jon Grantham, Steven Hayman and Andrew Shallue PDF
Math. Comp. 83 (2014), 899-915 Request permission


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 $\Lambda$.
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Additional Information
  • Jon Grantham
  • Affiliation: Institute for Defense Analyses, Center for Computing Sciences, 17100 Science Drive, Bowie, Maryland 20715
  • Email:
  • Steven Hayman
  • Affiliation: 1331 East Washington Street, Unit A, Greenville, South Carolina 29607
  • Email:
  • Andrew Shallue
  • Affiliation: Illinois Wesleyan University, 1312 Park St., Bloomington, Illinois 61701
  • MR Author ID: 805175
  • Email:
  • Received by editor(s): December 15, 2011
  • Received by editor(s) in revised form: May 24, 2012
  • Published electronically: July 9, 2013
  • Additional Notes: W. R. Alford passed away in 2003
    This research was supported by an Illinois Wesleyan University grant
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 899-915
  • MSC (2010): Primary 11Y16
  • DOI:
  • MathSciNet review: 3143697