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Mathematics of Computation

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

 

 

A new lower bound for odd perfect numbers


Authors: Richard P. Brent and Graeme L. Cohen
Journal: Math. Comp. 53 (1989), 431-437, S7
MSC: Primary 11A25; Secondary 11Y05, 11Y70
DOI: https://doi.org/10.1090/S0025-5718-1989-0968150-2
MathSciNet review: 968150
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Abstract: We describe an algorithm for proving that there is no odd perfect number less than a given bound K (or finding such a number if one exists). A program implementing the algorithm has been run successfully with $ K = {10^{160}}$, with an elliptic curve method used for the vast number of factorizations required.


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DOI: https://doi.org/10.1090/S0025-5718-1989-0968150-2
Article copyright: © Copyright 1989 American Mathematical Society