A019294(461)

[Hugo Pfoertner]

Don Reble wrote:
> 
> Lambert Klasen wrote:
> > any hint for stupid me, what kind of program you use,
> > to compute this so fast ?
> 
> I find that there's usually little factoring to do. When you compute
> Y=sigma(X) as a product of numbers, keep all of those numbers; and
> at the next step, factor them instead of Y.
> Also, Y's partial products are all (b^k-1)/(b-1), and usually their
> factors can be found at http://www.cerias.purdue.edu/homes/ssw/cun
> (I didn't use that, and so my program spent many minutes refactoring
> 2^263-1.)
> 
> --
> Don Reble  djr at nk.ca

It takes less than 1 s of CPU time to factor 2^263-1 on an old 800 MHz
Athlon using Dario Alpern's Java applet "Factorization using the
Elliptic Curve Method" at http://www.alpertron.com.ar/ECM.HTM , even if
the option "Use Cunningham tables on server" is not used.

14 821387 422376 473014 217086 081112 052205 218558 037201 992197 050570 
753012 880593 911807 = 23671 x 13 572264 529177 x 120 226360 536848
498024 035943 x 383725 126655 170964 501315 730676 446647 

Hugo Pfoertner