Factoring with the Quadratic Sieve on Large Vector Computers

摘要

The multiple polynomial version of the quadratic sieve factorization method was run on a Cyber 205 and on a NEC SX-2 vector computer. Various numbers in the 50 to 92 decimal digits range were factorized, as a contribution to the Cunningham project, Brent's Table of factors of Mersenne numbers, and a proof by Brent and Cohen of the nonexistence of odd perfect numbers below 10 to the 200th power. The NEC program is 5 to 10 times faster than the Cyber one, and 5 to 10 times faster than the Davis and Holdridge Cray X/MP program.