Factoring humongous Cunningham numbers

[jasong]

Mr. Silverman, if you're willing to accept the fact that I have zero knowledge of how ecm works, and you don't care that I don't care, I would be happy to give you a week or two of time on my lowly 1.75GHz Sempron.

Just post some ecm parameters and I can get on it right away.

Edit: I apologize, I didn't see post #6.

I'm going to attempt to get it running sometime tonight.

Edit2: Could someone post some stuff about filenames and how to use post #6 info. Sorry for my ignorance.

[jasong]

Mr. Silverman, could you please post more info about your curves? I learned the hard way that different B1, B2 values mean that a different number of curves is necessary.

Can I assume that your B1=1e6 means B2=8.4e8? (I printed out part of a web page a while back, not realizing B1/B2 parameters weren't set in stone. In the instance of these parameters it says 35-digits and 1100 curves. Is this correct? Or is B2=B1*100? Or are they both wrong?)

[rogue]

14273530385368339 is a factor of 389-. The cofactor is composite.

[R.D. Silverman]

Originally Posted by John Renze

The C87 cofactor of 3^636-2^363 factors thusly:

51367404262568392429656240517252067923 x 7705482404964763837578788370404060262063595624219

This factorization was found using Msieve v. 1.01.

Much obliged.

Bob

[R.D. Silverman]

Originally Posted by jasong

Mr. Silverman, could you please post more info about your curves? I learned the hard way that different B1, B2 values mean that a different number of curves is necessary.

Can I assume that your B1=1e6 means B2=8.4e8? (I printed out part of a web page a while back, not realizing B1/B2 parameters weren't set in stone. In the instance of these parameters it says 35-digits and 1100 curves. Is this correct? Or is B2=B1*100? Or are they both wrong?)

It is not important. I ran several hundred curves with B1 = 1M.
This should have cleared out factors to 30 digits. Run whatever curves you like.

[R.D. Silverman]

Originally Posted by John Renze

The factors of the C88 are:

1315651155909947565347700897218133001
1338208112877762546551051364373633349610010436196551

Thanks.

If anyone would like to see the entire set of tables (a^n +/- b^n)
for (a,b) = 1, a <=12, b < a, I will post them, but be warned:
the file is ~600Kb.

I do not work on them a lot.

Note that these tables are the "homogeneous" analogue of the Cunningham
tables.

[R.D. Silverman]

Originally Posted by Wacky

[SOAPBOX]
John,
I would like to thank you for completing this factorization.

Sometimes those of us who are committing our resources to more "cutting edge" problems

Actually, I don't do "cutting edge" anymore. I don't have the CPU
resources. I just clean up the "moderate sized" pieces that trail just
behind the leading edge...

I wish I did have the resources... I'd love to go after M1061..........
However, even if I had the sieving resources, solving the matrix for
this number will be a real problem...

Hey! perhaps we could get cajole IBM into lending "Big Blue" to do the
matrix once we get around to organizing the sieving????

I know Don Coppersmith. Perhaps I might ask him.

Bob

[xilman]

Originally Posted by R.D. Silverman

Thanks.

If anyone would like to see the entire set of tables (a^n +/- b^n)
for (a,b) = 1, a <=12, b < a, I will post them, but be warned:
the file is ~600Kb.

I do not work on them a lot.

Note that these tables are the "homogeneous" analogue of the Cunningham
tables.

I suggest that rather than post the tables, you post a URL to a site that holds them.

If you don't have them hosted anywhere, I'll volunteer to put them on my site if you wish.


Paul

[R.D. Silverman]

Originally Posted by xilman

I suggest that rather than post the tables, you post a URL to a site that holds them.

If you don't have them hosted anywhere, I'll volunteer to put them on my site if you wish.


Paul

We are behind a strict firewall. I will send them to you.

[smh]

Can somenody explain me how to create a SNFS polynomial for these numbers?

[xilman]

Originally Posted by R.D. Silverman

We are behind a strict firewall. I will send them to you.

Got them, thanks.

It will take me a little time to put them on the web as I need to convert your mail to separate files and then to write an HTML wrapper. I'll probably put a separate copy of the tables in my standard format too --- one designed to be easily parsed by people and by programs.

When the page is ready I'll post the URL here.


Paul