## A new lower bound for odd perfect numbers

100. R. P. Brent and G. L. Cohen,
A new lower bound for odd perfect numbers,
* Mathematics of Computation * 53 (1989), 431-437.
Microfiche supplement * ibid*, S7-24.
MR 89m:11008.
Abstract:
dvi (3K),
pdf (79K),
ps (28K).

Paper:
pdf (724K).

Supplement (the proof tree):
pdf (2037K).

## Abstract

We describe an algorithm for proving that there is no odd perfect number less
than a given bound *K* (or finding such a number if one exists).
A program
implementing the algorithm has been run successfully with
*K* = 10^{160},
with the elliptic curve method used for the vast number of factorizations
required.
## Comments

The proof tree has 3132 leaves and is available as a separate file
(see above).
For a sequel which extended the result to
*K* = 10^{300},
see Brent, Cohen and te Riele [116].
The integer factorizations used in the proofs are available
here.

Go to next publication

Return to Richard Brent's index page