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Journal Articles Mathematics of Computation Year : 2012

Odd Perfect Numbers are Greater than 10^1500

Pascal Ochem
Michael Rao

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.

Dates and versions

lirmm-00739245 , version 1 (06-10-2012)

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Pascal Ochem, Michael Rao. Odd Perfect Numbers are Greater than 10^1500. Mathematics of Computation, 2012, 81 (279), pp.1869-1877. ⟨10.1090/S0025-5718-2012-02563-4⟩. ⟨lirmm-00739245⟩
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