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A New Lower Bound for Odd Perfect Numbers

Richard P. Brent and Graeme L. Cohen
Mathematics of Computation
Vol. 53, No. 187 (Jul., 1989), pp. 431-437
DOI: 10.2307/2008375
Stable URL: http://www.jstor.org/stable/2008375
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A New Lower Bound for Odd Perfect Numbers
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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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