Odd perfect numbers are greater than

Authors:
Pascal Ochem and Michaël Rao

Journal:
Math. Comp. **81** (2012), 1869-1877

MSC (2010):
Primary 11A25, 11A51

Published electronically:
January 30, 2012

MathSciNet review:
2904606

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Abstract | References | Similar Articles | Additional Information

Abstract: Brent, Cohen, and te Riele proved in 1991 that an odd perfect number is greater than . We modify their method to obtain . We also obtain that has at least 101 not necessarily distinct prime factors and that its largest component (i.e. divisor with prime) is greater than .

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Additional Information

**Pascal Ochem**

Affiliation:
LRI, CNRS, Bât 490 Université Paris-Sud 11, 91405 Orsay cedex, France

Email:
ochem@lri.fr

**Michaël Rao**

Affiliation:
CNRS, Lab J.V. Poncelet, Moscow, Russia. LaBRI, 351 cours de la Libération, 33405 Talence cedex, France

Email:
rao@labri.fr

DOI:
https://doi.org/10.1090/S0025-5718-2012-02563-4

Received by editor(s):
March 27, 2011

Received by editor(s) in revised form:
April 14, 2011

Published electronically:
January 30, 2012

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.