Improved techniques for lower bounds for odd perfect numbers
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- by R. P. Brent, G. L. Cohen and H. J. J. te Riele PDF
- Math. Comp. 57 (1991), 857-868 Request permission
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 $N > {10^{300}}$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Math. Comp. 57 (1991), 857-868
- MSC: Primary 11A25; Secondary 11Y70
- DOI: https://doi.org/10.1090/S0025-5718-1991-1094940-3
- MathSciNet review: 1094940