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 = 10160,
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 = 10300,
see Brent, Cohen and te Riele [116].
The integer factorizations used in the proofs are available
here.
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