[QUOTE=akruppa]

Brief history: after sieving sq on the rational side in [30M, 70M] it turned out that a sieve region of 16394x8192 (gnfs-lasieveI14e) would use a lot of special-q values (about up to 150M) and probably produce a pretty large matrix.

[/QUOTE]


This surprises me. A bit.

For 5x^6-1, a typical rational norm will be somewhere around 10^45 to
10^48, while an algebraic norm will be 'typically' about 10^38 to 10^42.
It is usually better to run special q's on the side with the larger norm.
The algorithm works best when the norms we hope are smooth are as close
as possible on each side. For sq ~ 10^7, rational norm/sq will
be close to the algebraic norm. The opposite is not true; the norms
would be lopsided.

Yes, the norms on the algebraic side are a bit larger and the yield with sq on the algebraic side is a bit better, but the difference isn't that great. At sq=30M, alg. sq produce about 20.9 relations per sq, rat.sq about 24.6, about 18% more. As sq increases, the norms on the algebraic side grow faster, so the difference diminishes. With sq=70M, the yield is about 15.9 and 17.9, resp., about 12% difference.

I did most of the sieving on the algebraic side on the cluster and had a few scripts to start jobs on nodes. I simply used them until sq=70M, the same as on the rational side. That wasn't optimal... but I was being lazy.

Alex

The figures in my last post were done with the smaller sieve region. With the larger region, the size of the norms shifts towards the algebraic side some more, and the yield at SQ=70M is almost exactly the same: about 32.9 vs 32.7/sq. So it didn't really matter which side I did at these high sq.

Alex

Ah well, all good things must end. Usage of the cluster has increased so much that they inquired who is actually using it for research projects, and since my diploma thesis is long finished by now, I don't really have a good excuse to keep using it. They'll delete my account there shortly. Fortunately they agreed to let me finish the 5,349- matrix yet! Fingers crossed that the dependencies it'll find will be useful, after all my filter hacking...

My time with this cluster was another case where I got far more than I had hoped for, so no hard feelings here. I would have liked to finish 3+ to exponent 500, but there's still time for that later. Besides, I have to prepare for my last two finals and hunting idle time on the cluster was quite a distraction. Maybe it's for the better this way...

Due to the exams, I will rarely be online until April.

Alex

[QUOTE=akruppa]Ah well, all good things must end. Usage of the cluster has increased so much that they inquired who is actually using it for research projects, and since my diploma thesis is long finished by now, I don't really have a good excuse to keep using it.

Due to the exams, I will rarely be online until April.

Alex[/QUOTE]

To the tune of a familiar American folk song......


Oh, grad strudents come and grad students go,
And the best we have is gone I know,
But if he don't come back this spring,
We'll have to stop the factoring!

The matrix is about 50% done now. It probably will be finished some time in early march.

Alex

Alex,

Update?

The matrix is 87.7% done. Will probably take another week.

Alex

The matrix step is completed now. The sqrt step will be a bit of a headache again, I will need to adapt it to 31 bit primes first. It also likes to use primes just above 10^9 for CRT and I forgot to remove relations containing such primes during the filtering, so I'll have to find a different set of CRT primes to use. I have no idea how difficult that will be and I'm rather occupied atm, so the factors may take a while yet - sorry!

Alex

Another brief update: making sqrt use different CRT primes was not hard at all, only a constant in the code needed to be changed. I found a large enough interval of primes that do not appear among my relations so I'm using those for CRT now. Unfortuntately, the program still aborted with a failed assertion. I'll have to check whether the 31st bit of primes gets mangled somewhere, but due to little spare time, this will take quite a while.

Alex

Update time yet?