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Mathematics of Computation

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



Improved techniques for lower bounds for odd perfect numbers

Authors: R. P. Brent, G. L. Cohen and H. J. J. te Riele
Journal: Math. Comp. 57 (1991), 857-868
MSC: Primary 11A25; Secondary 11Y70
MathSciNet review: 1094940
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Abstract: If N is an odd perfect number, and ${q^k}||N$, q prime, k even, then it is almost immediate that $N > {q^{2k}}$. We prove here that, subject to certain conditions verifiable in polynomial time, in fact $N > {q^{5k/2}}$. Using this and related results, we are able to extend the computations in an earlier paper to show that $N > {10^{300}}$.

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Article copyright: © Copyright 1991 American Mathematical Society