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Odd Perfect Numbers are Greater than 10^1500
Journal article   Open access   Peer reviewed

Odd Perfect Numbers are Greater than 10^1500

Pascal Ochem and Michael Rao
Mathematics of Computation, Vol.81(279), pp.1869-1877
2012

Abstract

Brent, Cohen, and te Riele proved in 1991 that an odd perfect number N is greater than 10^300. We modify their method to obtain N > 10^1500. We also obtain that N has at least 101 not necessarily distinct prime factors and that its largest component (i.e. divisor p^a with p prime) is greater than 10^62.
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https://doi.org/10.1090/S0025-5718-2012-02563-4View
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