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 R.D. Silverman 2005-06-30 11:55

2,749+

2,749+ has been completed:

2,791+ is sieving.

2,749+ C189 = p58.p132

p58 = 1067740385407532831676124118528135895750892746743123583547
p132 = 265168210875294435131691485888315426328518887962256780931238822948289856657586504113363655596519745405902488698615900864762882650843

 Wacky 2005-06-30 12:15

Thanks for the factor, Bob. Good work! I'm sure that Sam will be happy to get it.

Just to make sure that we don't confuse casual readers, 2,749+ and 2,791+ are numbers that Bob is doing independently of the NFSNet structure.

NFSNet is currently working on 2,751+ and will then quickly do 2,760+.

Richard

 R.D. Silverman 2005-06-30 13:03

[QUOTE=Wacky]Thanks for the factor, Bob. Good work! I'm sure that Sam will be happy to get it.

Just to make sure that we don't confuse casual readers, 2,749+ and 2,791+ are numbers that Bob is doing independently of the NFSNet structure.

NFSNet is currently working on 2,751+ and will then quickly do 2,760+.

Richard[/QUOTE]

I assume you are doing 2,760+ with GNFS? It is a borderline choice.

Why do this one ahead of 2,719+ and 2,736+??? These latter two are
"first holes".

 Wacky 2005-06-30 14:35

I'm doing 2,760+ next because that is the one that Paul set up. You'll have to ask him why he chose it in preference to one of the others. I don't know if it is the case here, but sometimes we have skipped some of the easier ones to leave more managable ones to those with smaller sieving capacity.

The original intent was to do it by gnfs, partly to help some less knowledgable people realize that NFSNet can do either gnfs or snfs since they are essentially the same once you have chosen the polynomials.

After Don and ? did some searching, I think that they concluded that the SNFS was just as good. It seems that Paul went with

M = 2^152
M -x
1 -x +x^2 -x^3 +x^4

 xilman 2005-06-30 15:39

[QUOTE=Wacky]I'm doing 2,760+ next because that is the one that Paul set up. You'll have to ask him why he chose it in preference to one of the others. I don't know if it is the case here, but sometimes we have skipped some of the easier ones to leave more managable ones to those with smaller sieving capacity.

The original intent was to do it by gnfs, partly to help some less knowledgable people realize that NFSNet can do either gnfs or snfs since they are essentially the same once you have chosen the polynomials.

After Don and ? did some searching, I think that they concluded that the SNFS was just as good. It seems that Paul went with

M = 2^152
M -x
1 -x +x^2 -x^3 +x^4[/QUOTE]

Warning: I've just got back from the other Cambridge and haven't slept properly in several days, so I not be entirely coherent.

I think we decided that it would be a Good Thing to clear the 2+ and 2- tables to 768 bits. There are only a few of these left and, to me, it doesn't seem to matter that much whether any particular order is chosen to achieve that goal.

As Richard said, NFSNET has somewhat greater resources than some people/teams and it makes sense for us to concentrate on somewhat harder factorizations.

What with a business trip and serious hardware problems, I had to set up the parameters for the next NFSNET project in rather a hurry. So that the params were certain to be ready in time I didn't spend a long time mulling over alternatives.

Don and JesH found that the quartic SNFS was rather more productive than the best GNFS quintic polynomial they discovered. Though not markedly so, it was still more than "marginally" better. I based my choice on their discovery.

Paul

 junky 2005-07-05 02:37

Just as curiosity:
What's the pending projects for NFSnet?
1) 2,751+
2) 2,760+
3) 2,719+
4) 2,736+
what's next after?
any expectations for these projects?

And the current version of the client has not changed since a couple of months now. Is there any plans for this? I think an offline client is crucial, which could make a huge impact in the process if sieving.
I know Bob has started something about an offline client for *nix platforms, anything for windows?