On Wednesday 27 February 2002 05:07, you wrote: > Well anything that can increase the speed of TF by even a wee amount is > welcome by me.
Unfortunately there is no impact on trial factoring. The technique suggested is an improvement requiring specialized hardware of a technique which is only effective on numbers which are exceptionally hard to factor. Trial factoring would still be employed to dig out any small factors, as it's a great deal more efficient to remove these before resorting to more advanced techniques. The specialized hardware can, of course, be emulated in a general-purpose computer. The paper is not particularly clear on whether an implementation of the new algorithm would be any more efficient than the existing NFS method (which is also defined in terms of specialised hardware) when a general-purpose computer emulation is employed. I guess that depends a great deal on the quality of the emulation. In terms of the work on Mersenne numbers, assuming the theoretical gains predicted in the paper can be realized, then the main effects would be: 1. an increase in the rate at which the NFS people are factoring "awkward" Mersenne numbers; 2. a possible corresponding decrease in the depth to which it's worth proceeding using ECM before handing awkward numbers over to the NFS squad. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
