Discussion related to cado-nfs

[Aurore Guillevic <aurore.guillevic@inria.fr>]

Hi,
The strategy to get a medium-size factor is to use GMP-ECM, with the 
parameters at https://members.loria.fr/PZimmermann/records/ecm/params.html
The 6-th row gives:
for i in `seq 1 5208` ; do echo 
122707855552185828468257427836864283300563571915184717192876562407609081222481009431414764530405548369855861509454229893234271790119941689194939718305389933643 
| gmp-ecm 11000000 >> gmp-ecm-6.txt ; done

Then grep the output file for `Factor found` and you will get the 
45-digit factor, with another 114 digit composite cofactor. It takes 
some hours too (should be parallelized).

A. Guillevic.


On 7/31/25 08:48, hermann@stamm-wilbrandt.de wrote:
> On 2025-07-30 23:54, Greg Marks wrote:
> > In my experience, cado-nfs does work for non-semiprime input. In 2014
> > I ran cado-nfs-2.0 to successfully factor the number
> >
> >
> > 122707855552185828468257427836864283300563571915184717192876562407609081222481009431414764530405548369855861509454229893234271790119941689194939718305389933643. 
> >
> >
> > The final cado-nfs output was the three prime factors, separated
> > by spaces.  (I should say that I have not tested this on more recent
> > versions of cado-nfs.)
> >
> > Incidentally, due to the relatively small size of the smallest prime
> > factor of my number, ...
> Thanks,
>
> "relatively small size" is bigger than I thought.
> What is that prime factor?
>
> I did run this little GP script for more than 6 hours without factor 
> found:
>
> hermann@7950x:~$ gp -q
> ? 
> o=2;forprime(p=3,,if(n%p==0,print(p);quit());if(p\10^8!=o\10^8,o=p;print1(".")))^C
>   ***   user interrupt after 6h, 11min, 21,939 ms
>
> I counted the number of dots printed, and the smallest factor is not 
> smaller than
>
> (128*114+16)*10^8 = 1460800000000
>
> Since single threaded, the AMD 7950X CPU did run a >5.5GHz ...
>
> Regards,
>
> Hermann.