Factoring humongous Cunningham numbers

[jyb]

Originally Posted by xilman

I'd been meaning to make that request myself but hadn't got a round tuit, so thanks.

It would be nice to record the work in the server but your choice of "useless" is a little emphatic IMO. Slightly sub-optimal may be more appropriate. Unless Bob has (a) vastly more resources than I suspect and [(b) hasn't been reporting all his findings or (c) has been amazingly unlucky], his efforts are unlikely to persuade the server from handing out tasks with B1=43M for some substantial time yet.

Paul

Sure, but if his work hasn't been uniform (i.e. same number of curves on all composites), then there may be some subset of numbers which should no longer be handed out at B1=43M. But nonetheless you are correct; suboptimal would have been a more accurate description.

[PhilF]

I am kind of new at this and have a few questions.

I have been working on the numbers in the file you get when you download the "Cunningham input list" from http://webloria.loria.fr/~zimmerma/ecmnet/.

Are these numbers included in the work the server hands out, or are they a completely different set of numbers?

Also, that page recommends B1=43M. But in GMP-ECM's "INSTALL-ecm" file I found a reference that recommends B1=110M. I just assumed that the 43M recommendation was out of date, so I have been using 110M and higher.

I'm just getting started here and have not run enough curves to amount to a hill of beans, so I haven't reported them. Since I am running only a few curves on lots of different numbers, is there a point where I probably should report the number of curves I have run?

[R.D. Silverman]

Originally Posted by PhilF

I am kind of new at this and have a few questions.

I have been working on the numbers in the file you get when you download the "Cunningham input list" from http://webloria.loria.fr/~zimmerma/ecmnet/.

Are these numbers included in the work the server hands out, or are they a completely different set of numbers?

Also, that page recommends B1=43M. But in GMP-ECM's "INSTALL-ecm" file I found a reference that recommends B1=110M. I just assumed that the 43M recommendation was out of date, so I have been using 110M and higher.

I would recommend B1 = 260M or higher. It is improbable that there are
any factors left under 55 digits.

I would select a limited subset. For example, the base 12 composites.
You might want to ask Bruce which numbers he has done the least.
The 2LM composites might be a good choice. I ran 1000 curves
on each of them with B1 = 500M. It took 6 months.

[jyb]

Originally Posted by PhilF

I am kind of new at this and have a few questions.

I have been working on the numbers in the file you get when you download the "Cunningham input list" from http://webloria.loria.fr/~zimmerma/ecmnet/.

Are these numbers included in the work the server hands out, or are they a completely different set of numbers?

Also, that page recommends B1=43M. But in GMP-ECM's "INSTALL-ecm" file I found a reference that recommends B1=110M. I just assumed that the 43M recommendation was out of date, so I have been using 110M and higher.

I'm just getting started here and have not run enough curves to amount to a hill of beans, so I haven't reported them. Since I am running only a few curves on lots of different numbers, is there a point where I probably should report the number of curves I have run?

And to answer some other questions which Bob didn't address:

- The numbers to which this thread applies are called the Homogeneous Cunningham numbers, and information about them can be found at http://www.leyland.vispa.com/numth/f.../anbn/main.htm. These are distinct from the (just plain) Cunningham numbers.

- The ECMnet server referred to here only hands out Homogeneous Cunningham numbers.

- If you use this ECMnet server, then you don't need to do any reporting at all, the server tracks your work for you.

- The Cunningham input list you've downloaded includes only the plain Cunningham numbers. As Bob said, they have been ECM'd to very high values already. I'm not aware of any central repository for information on current curve counts, but Bruce probably has the best such information. You are very unlikely to find any factors using a B1 of 110M.

- If you do run ECM on the Cunningham numbers, and you have sufficient resources to run a lot of them at high B1, then reporting it would be a good idea. To whom? I'm not sure. I suppose you can start by creating a thread in the Cunningham Tables subforum of this forum: http://mersenneforum.org/forumdisplay.php?f=51. I think the relevant folks would see it there. But again, you would have to be able to run many thousands of curves with a B1 >= 250M before anybody is likely to take notice.

[jyb]

Originally Posted by R.D. Silverman

Sure.

I've been running each number for one day with my limited number of machines.

This typically means about 800 curves with B1 = 200M. The exact number
of curves varies from day to day owing to machine availability.

Thanks. Do you have a record of the specifics which you can share with Paul?

[frmky]

As Lionel pointed out to me, the Fibonacci and Lucas numbers in the range of NFS@Home 14e sieve will likely run out in mid-to-late summer, so we are considering other sources of numbers. Personally I find this to be an attractive list, but they haven't really had enough ECM. Would it be too much to ask to have a fraction of these, especially SNFS difficulties about 220 and above, ECM'ed to at least t50 by then? Perhaps by teaming with yoyo@home's ECM project if needed?

[R.D. Silverman]

Originally Posted by frmky

As Lionel pointed out to me, the Fibonacci and Lucas numbers in the range of NFS@Home 14e sieve will likely run out in mid-to-late summer, so we are considering other sources of numbers. Personally I find this to be an attractive list, but they haven't really had enough ECM. Would it be too much to ask to have a fraction of these, especially SNFS difficulties about 220 and above, ECM'ed to at least t50 by then? Perhaps by teaming with yoyo@home's ECM project if needed?

I have run 700 to 800 curves with first limit 200x 10^6 on all
composites less than 208 digits. I am continuing the search.

[chris2be8]

Originally Posted by frmky

As Lionel pointed out to me, the Fibonacci and Lucas numbers in the range of NFS@Home 14e sieve will likely run out in mid-to-late summer, so we are considering other sources of numbers.

There are plenty of composites in the Brent tables in that size range. I've done most of the ones below 220 digits SNFS difficulty. I don't know how much ECM they have had, but I've only found two factors below 50 digits, so they have probably had more that T50 done.

Chris

[xilman]

Originally Posted by frmky

As Lionel pointed out to me, the Fibonacci and Lucas numbers in the range of NFS@Home 14e sieve will likely run out in mid-to-late summer, so we are considering other sources of numbers. Personally I find this to be an attractive list, but they haven't really had enough ECM. Would it be too much to ask to have a fraction of these, especially SNFS difficulties about 220 and above, ECM'ed to at least t50 by then? Perhaps by teaming with yoyo@home's ECM project if needed?

Should be straightforward for me to produce some (G)CW candidates in that range. The next batch of work at yoyo@home should start in a week or two and finish in your desired time frame.

Please let me know if you would take some on and I'll re-arrange ECM priorities accordingly.

[Yamato]

A lucky ECM result after 6 months:

10^236+9^236  prp67 factor: 2970502746365749876818923808989713022319848931047956587856682374457
B1 = 11e7
sigma = 1323877938
group order = 2^2 * 3^4 * 5 * 139 * 229 * 257 * 9343 * 112111 * 269617 * 447331 * 1780201 * 6715523 * 7861031 * 31025243 * 608523161

[xilman]

Originally Posted by Yamato

A lucky ECM result after 6 months:

10^236+9^236  prp67 factor: 2970502746365749876818923808989713022319848931047956587856682374457
B1 = 11e7
sigma = 1323877938
group order = 2^2 * 3^4 * 5 * 139 * 229 * 257 * 9343 * 112111 * 269617 * 447331 * 1780201 * 6715523 * 7861031 * 31025243 * 608523161

Wow!

Have you told the other Paul about this one?