Odd Perfect Numbers are Greater than 10^1500

Pascal Ochem 1 Michael Rao 2
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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://hal-lirmm.ccsd.cnrs.fr/lirmm-00739245
Contributor : Pascal Ochem <>
Submitted on : Saturday, October 6, 2012 - 5:18:12 PM
Last modification on : Thursday, February 7, 2019 - 4:59:37 PM

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  • HAL Id : lirmm-00739245, version 1

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Pascal Ochem, Michael Rao. Odd Perfect Numbers are Greater than 10^1500. Mathematics of Computation, American Mathematical Society, 2012, 81 (279), pp.1869-1877. ⟨lirmm-00739245⟩

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