Discussion related to cado-nfs

[Markus Tervooren <mail@markustervooren.de>]

Hi Paul,

thanks you for your insights on this topic.

With a target-density of 200 the matrix looks like this:

Final matrix has N=64337429 nc=64337178 (251) W=12878433733

bwc is expected to take quite a bit longer:

krylov: N=4000 ; ETA (N=2011000): Sat Nov  9 18:15:39 2024 [1.559 s/iter]

I'll continue with the density 141 matrix this time.

Markus

Am 04.10.24 um 09:35 schrieb Paul Zimmermann:
>         Hi Markus,
>
> it's been a long time I did not do such a large factorization.
>
> > Date: Thu, 3 Oct 2024 21:31:24 +0200
> > From: Markus Tervooren <mail@markustervooren.de>
> >
> > Dear Paul,
> >
> > I successfully obtained a suitable matrix and have now begun the BWC step.
> >
> > Sieving parameters were:
> >
> > -q0 1000000 -q1 920000000 -A 31 -lim0 300000000 -lim1 300000000 -lpb0 35
> > -lpb1 35 -mfb0 86 -mfb1 96 -ncurves0 20 -ncurves1 20
> usually we try to set lim1 larger than lim0, since the norms on the algebraic
> side are larger. You could try for example lim0=200000000 and lim1=400000000.
>
> > For a total of 3B raw relations. After dup2, 1.9B relations remained.
> > Including all relations up to 35 bits resulted in a significantly better
> > matrix compared to using only 34 bits - these were removed after sieving.
> >
> > The purge process reduced the total to 249 million relations:
> >
> > Step 0: only singleton removal
> > Sing. rem.: begin with: nrows=1917941307 ncols=1948512258
> > excess=-30570951 at 2883.09
> > Sing. rem.:   iter 001: nrows=1155353090 ncols=1012751300
> > excess=142601790 at 4037.84
> > Sing. rem.:   iter 002: nrows=976499437 ncols=821895684 excess=154603753
> > at 4521.78
> > Sing. rem.:   iter 003: nrows=929047533 ncols=773453347 excess=155594186
> > at 4857.31
> an excess of 17% is quite nice!
>
> > Sing. rem.:   iter 002: nrows=249083636 ncols=249083416 excess=220 at
> > 56595.46
> > Sing. rem.:   iter 003: No more singletons, finished at 56675.36
> >
> > Matrix: total 71851914 rows 71851662 cols 10096684980 coeffs
> this corresponds to an average density of 141 non-zero elements per row.
> BWC is quite efficient for larger densities. You could try target-density 170
> or even 200. It would be interesting to build the corresponding matrices
> (merge is quite fast), and start BWC to see if it would take less than 45 
> days.
>
> > krylov: N=60000 ; ETA (N=2248000): Wed Oct 30 03:07:17 2024 [1.100 s/iter]
> >
> > Expecting factors in about 45 days. The composite is part of aliquot
> > sequence 162126, index 4412.
> >
> > Suggestions for better parameters are always welcome.
> yes, feel free to propose a patch for params.c210, which dates from 7 years
> ago.
>
> Paul

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