Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Odd perfect numbers are greater than $10^{1500}$

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 $10^{62}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 11A25, 11A51

Retrieve articles in all journals with MSC (2010): 11A25, 11A51

Additional Information

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

Michaël Rao
Affiliation: CNRS, Lab J.V. Poncelet, Moscow, Russia. LaBRI, 351 cours de la Libération, 33405 Talence cedex, France
MR Author ID: 714149

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.