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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.

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Odd perfect numbers have a prime factor exceeding $10^8$
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by Takeshi Goto and Yasuo Ohno PDF
Math. Comp. 77 (2008), 1859-1868 Request permission


Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding $10^7$. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding $10^8$.
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Additional Information
  • Takeshi Goto
  • Affiliation: Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, 278-8510, Japan
  • Email:
  • Yasuo Ohno
  • Affiliation: Department of Mathematics, Kinki University Higashi-Osaka, Osaka 577-8502, Japan
  • Email:
  • Received by editor(s): December 13, 2006
  • Received by editor(s) in revised form: February 26, 2007
  • Published electronically: February 12, 2008
  • Additional Notes: This work was supported by Computing and Communications Center, Kyushu University
    The second author was supported in part by JSPS Grant-in-Aid No. 15740025 and No. 18740020
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 77 (2008), 1859-1868
  • MSC (2000): Primary 11A25, 11Y70
  • DOI:
  • MathSciNet review: 2398799