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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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Submitted on : Saturday, October 6, 2012 - 5:18:12 PM
Last modification on : Friday, September 30, 2022 - 4:13:58 AM


  • HAL Id : lirmm-00739245, version 1


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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