A new lower bound for odd perfect numbers

Author:

Brent Richard P.,Cohen Graeme L.

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 K = {10^{160}} , with an elliptic curve method used for the vast number of factorizations required.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference15 articles.

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2. R. P. Brent, "Some integer factorization algorithms using elliptic curves," Australian Computer Science Communications, v. 8, 1986, pp. 149-163.

3. R. P. Brent, G. L. Cohen & H. J. J. te Riele, An Improved Technique for Lower Bounds for Odd Perfect Numbers, Report TR-CS-88-08, Computer Sciences Laboratory, Australian National University, August 1988.

4. Contemporary Mathematics;Brillhart, John,1983

5. M. Buxton & S. Elmore, "An extension of lower bounds for odd perfect numbers," Notices Amer. Math. Soc., v. 23, 1976, p. A-55.

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