A new lower bound for odd perfect numbers
Richard P. Brent, Graeme L. Cohen · Mathematics of Computation · 1989
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.