[QUOTE=LaurV;268733]I don't, because I did not see any. It seems that only "over 70" are added to that list, most probably "under 70" are automatically taken care by the server without adding them to that list. Or at least that was my impression after spending a couple of hours on database yesterday. In fact it is said somewhere there that the exponents under 70 digits are factored by I don't know which machine on that list. So I took care yesterday (gmt+7 here) of everything that appeared under 82 bits. That was fun, and quite suitable task for me, who I am quite impatient and don't like waiting days to see some factors :D[/quote]The composite queue looks to be under control right now. Sometimes, though, the queue can be quite long, with composites down to the mid 30-50 digit range (really only a problem when someone is spamming the factor tables really heavily....)
[quote](running yafu and Dario's applet, manually, in "stealing clocks" mode, that means: they don't have their own core, as all cores are busy with other - longer - tasks)[/quote]Thank you for your contribution. I look on factoring what I can as the toll I pay for the use I get out of the DB (check out the aliquot [url="http://www.mersenneforum.org/forumdisplay.php?f=90"]subforum[/url] to see where I hang my hat).

If you ever want to devote some more time to work that needs doing, let us know. The other nice thing to contribute is primality certificates for primes >300 digits, but those take a bit more time and effort.[quote]P.S. love your avatar![/QUOTE]Thanks, I tried on quite a few before I settled on this one.....some days that's the way I really feel.

PS. I see Syd hit reply a little ahead of me.

[QUOTE=Syd;268736]I'm wondering if it would make sense to factor some numbers around 90 digits with a good snfs poly using snfs. Just factored (2^298*419+911)/281 (90 digits) as a test, it took ~5 minutes to get 1M relations + 1 minute for postprocessing using msieve, yafu/siqs took >30 minutes.[/QUOTE]If you could come up with a quick & easy automated way, I'd say go for it, otherwise it might be quicker/easier to just use msieve or yafu for the small numbers.

When I have my system factoring, I just run msieve in batch mode, since it can sometimes get lucky hits with the "deep ECM" option. Nothing like factoring 80+ digit numbers in <30 secs!

Just out of curiosity, is there a snfs poly for terms like

a^x+b^x, a != b or
x^y+y^x ?

I'm trying to improve the poly generator but couldnt come up with any.

[QUOTE=Syd;268858]Just out of curiosity, is there a snfs poly for terms like

a^x+b^x, a != b or
x^y+y^x ?[/QUOTE]

They could both be handled as a^x+c with a very large constant term c0 that you would compensate for with a large skew. We need somebody more knowledgeable than me to say whether or not these are likely to be good polynomials.

x "+" c0

.."?"..

[url]http://factordb.com/index.php?id=1100000000442370817[/url]

0..+
`10000000000000000000000000000000000000000000000000063711591624522670185790732155277577204929976855347`*10

..

[url]http://factordb.com/index.php?id=1100000000442371243[/url]

(+2*?)

[QUOTE=Syd;268858]Just out of curiosity, is there a snfs poly for terms like

a^x+b^x, a != b or
x^y+y^x ?

I'm trying to improve the poly generator but couldnt come up with any.[/QUOTE]

Yes. For a^x+b^x, with b < a, if a and b are not coprime take out the common factor, then treat it just like a^x+1. However, rather than X-a^(x/d), the linear poly will be b^(x/d) X - a^(x/d). All the common tricks with x divisible by 3, 5, 7, 11, or 13 work as usual.

For x^y+y^x, see snfspoly.c at [URL="http://tech.groups.yahoo.com/group/xyyxf/files/"]http://tech.groups.yahoo.com/group/xyyxf/files/[/URL].

[QUOTE=frmky;268879]Yes. For a^x+b^x, with b < a, if a and b are not coprime take out the common factor, then treat it just like a^x+1. However, rather than X-a^(x/d), the linear poly will be b^(x/d) X - a^(x/d). All the common tricks with x divisible by 3, 5, 7, 11, or 13 work as usual.

For x^y+y^x, see snfspoly.c at [URL="http://tech.groups.yahoo.com/group/xyyxf/files/"]http://tech.groups.yahoo.com/group/xyyxf/files/[/URL].[/QUOTE]

You can also find several examples of polys for a^x +/- b^x (and a few examples how to calculate them) in the [URL="http://www.mersenneforum.org/showthread.php?t=5722"]homogeneous cunningham numbers thread[/URL].

Thank you, this is exactly what I was looking for!

Note that snfspoly generates degree 5 polynomials: you may want to modify it to generate degree 6 polynomials.

[QUOTE=Syd;268907]Thank you, this is exactly what I was looking for![/QUOTE]One thing: the SNFS polys are missing a "skew" value. You might add something for those that don't know how to set a value....

[QUOTE=schickel;268985]One thing: the SNFS polys are missing a "skew" value. You might add something for those that don't know how to set a value....[/QUOTE]

R.D.Silverman has posted it [URL="http://www.mersenneforum.org/showpost.php?p=266499&postcount=7"]here[/URL] with a hint to read his paper:

[QUOTE]Optimal Parameter Selection for SNFS, J. Math. Cryptology

Computing the skew is easy. No need to guess.

Let the polynomial be a_n x^n + .... + a_0.
Set the skew to (a_0/a_n)^1/n [or its reciprocal depending on how the
code uses it] [/QUOTE]