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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.


Factoring large integers
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by R. Sherman Lehman PDF
Math. Comp. 28 (1974), 637-646 Request permission


A modification of Fermat’s difference of squares method is used for factoring large integers. This modification permits factoring n in $O({n^{1/3}})$ elementary operations, where addition, subtraction, multiplication, division, or the extraction of a square root is considered as an elementary operation. A principal part is played by the use of a dissection of the continuum similar to the Farey dissection. This has been programmed for $n \leqq 1.05 \times {10^{20}}$ on the CDC 6400.
    G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, London, 1960. F. W. Lawrence, "Factorisation of numbers," Messenger of Math., v. 24, 1895, pp. 100-109.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Math. Comp. 28 (1974), 637-646
  • MSC: Primary 10A25
  • DOI:
  • MathSciNet review: 0340163