Discussion related to cado-nfs

[Paul Zimmermann <Paul.Zimmermann@inria.fr>]

       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