Factoring - a few questions?
 

I was wondering about a couple of things -
Out of interest, how many 26-27 million exponents have to be run before we expect a factor to be found - 1 in 10 to 15? and how many bits is this most likely to be found in i.e. 2^67 because it has the most numbers?
Also, if Primenet runs out of pre-factored exponents, will it just go ahead and instruct clients to factor the numbers before LL-ing if 'run first time exponents' is selected? (and just factoring, not P1?) Should do anyway - in that case no probs.
I was taking a look at Primenet and at the moment it seems that the LL wave is slowly gaining on the factoring wave (I can't be sure of the rate because it's hard to tell without manually checking over time myself) - but when factoring hits the magic 28.13 million (in about 6 months?) and the next tier 2^68 is needed this will slow tf-ing by about half and mean that the LL gains at double the closing speed. I know that on my factoring machine as it's not a P4 it is not an efficient use of its time to factor beyond 2^67 (because tf-ing is more efficient above 2^65 on a P4) and I'll probably have to move it onto something else.

Hope someone can comment
Thanks
(Minty)

[QUOTE]Out of interest, how many 26-27 million exponents have to be run before we expect a factor to be found - 1 in 10 to 15? and how many bits is this most likely to be found in i.e. 2^67 because it has the most numbers?[/QUOTE]Your estimate is about right, but the factors are more even across the bit-levels. From the prime95 help file: "Looking at past factoring data we see that the chance of finding a factor between 2^x and 2^(x+1) is about 1/x." So if factoring is from 2^62 to 2^67, the chance of finding a factor would be 5/66 or 7.6%. Which means I've been a bit unlucky so far as my success rate is only 5.9%.

[QUOTE]Also, if Primenet runs out of pre-factored exponents, will it just go ahead and instruct clients to factor the numbers before LL-ing if 'run first time exponents' is selected?[/QUOTE]Yes - clients will be given assignments where they do the TF and P-1 before starting the LL test.

[QUOTE]when factoring hits the magic 28.13 million (in about 6 months?) and the next tier 2^68 is needed this will slow tf-ing by about half and mean that the LL gains at double the closing speed.[/QUOTE]Right again - it will make a big difference. It feels like not so long ago that Primenet passed the limit at 21.59M and I finally took a P166 off TF!

Other factors will moderate the impact, although I haven't quantified them. Leading up to 28M, TF will actually become slightly quicker, while LL testing always takes longer for larger exponents, and has also just passed a limit for a larger FFT size which will slow it down some more. And of course George can adjust the thresholds in new versions of the client for the default work it will ask for, to keep the three streams flowing. (We don't want double-checking to fall further behind, do we!)

If you do take that machine off TF, you could put it onto LMH...

Hope this helps!

Thanks very much for the speedy and informative reply - its really appreciated.
I don't know what the best alternative DC project is - GIMPS is rock solid and very understandable, so it's a favourite for me (SoB is a little less so and seems to have some client issues). I tend not to like science/bio projects because there's always politics in the background - i.e. DF is going down soon, and I don't think we'll ever find ET!. Crypto is pretty much dead as all the quick ones are gone (D.net's a 900 yr end and md5crk is gone too). Zetagrid will probably go down after January - there are plenty of Maths ones, but to find something a little special is hard for me. NFSNet looks OK - but requires some discipline and I'm not sure exactly what the achievements are, and Lucas is still down - will keep looking anyhow and in the meantime will factor on!
Thanks again!
Mints

[QUOTE=Unregistered]Thanks very much for the speedy and informative reply - its really appreciated.
I don't know what the best alternative DC project is - GIMPS is rock solid and very understandable, so it's a favourite for me (SoB is a little less so and seems to have some client issues). I tend not to like science/bio projects because there's always politics in the background - i.e. DF is going down soon, and I don't think we'll ever find ET!. Crypto is pretty much dead as all the quick ones are gone (D.net's a 900 yr end and md5crk is gone too). Zetagrid will probably go down after January - there are plenty of Maths ones, but to find something a little special is hard for me. NFSNet looks OK - but requires some discipline and I'm not sure exactly what the achievements are, and Lucas is still down - will keep looking anyhow and in the meantime will factor on!
Thanks again!
Mints[/QUOTE]

You could try ECMNET. Help find factors of 2^n+1 and 2^n-1 so we don't
waste time factoring numbers with NFS that could more easily be done with
ECM. :banana:

See:[url]http://webloria.loria.fr/~zimmerma/records/ecmnet.html[/url]
and:[url]http://www.mersenne.org/ecm.htm[/url]


Or, if you want something OFFLINE, I could send my NFS code (source!)
and you could help finish 2^667+ and 2^689+.

Bob

Thanks for the suggestions Bob - lots of helpful people on this forum :-)
I think I'll give ECMNet a go when the new client is released, which is hopefully quite soon. (Fortunately I've got broadband so I'm on all the time!) I've always shied away from projects in the past where I've had to compile the source as I've no knowledge whatsoever on what to do in Windows (XP), and to make sure it's running efficiently on a particular architecture could be tricky for me! Hopefully the new client will come in .exe format (maybe even with athlon/P4 optimisations? or maybe they're not necessary). Anyway, I'll keep a lookout and see what comes along,
All the best
Minty

It will still be a couple of weeks before I release the new client. My beta testers have asked for a few changes, so I will be working on those and trying to get those tested.

I like the ECM factoring because the difficulty of finding a factor makes each discovery quite exciting, but the time between discoveries is not so long that I become discouraged.

I have been doing ECM for about six months on the base two Cunningham tables and in that time have found three factors of 43, 45, and 47 digits. I am using a Celeron 2.4, a P4 2.4, plus two old i586 class machines. Athlons are probably more efficient overall but there are some numbers in these tables where a P4 with Prime95 can be put to very good use.

[QUOTE=Unregistered]Thanks for the suggestions Bob - lots of helpful people on this forum :-)
I think I'll give ECMNet a go when the new client is released, which is hopefully quite soon. (Fortunately I've got broadband so I'm on all the time!) I've always shied away from projects in the past where I've had to compile the source as I've no knowledge whatsoever on what to do in Windows (XP), and to make sure it's running efficiently on a particular architecture could be tricky for me! Hopefully the new client will come in .exe format (maybe even with athlon/P4 optimisations? or maybe they're not necessary). Anyway, I'll keep a lookout and see what comes along,
All the best
Minty[/QUOTE]

I can provide NFS binaries for Windows, if you are interested.

[QUOTE=Unregistered]Zetagrid will probably go down after January[/quote]

Maybe even earlier - when the recent proof of the Riemann Hypothesis is correct.

[quote]NFSNet looks OK - but requires some discipline and I'm not sure exactly what the achievements are[/QUOTE]

The only things that disturb a bit are the need to be online every hour and to close the program when shutting down the computer.
The achievements are the factorizations of several numbers with up to 212 digits so far:
[url]http://www.nfsnet.org/announcements.html[/url]

The good thing is that the time to completion can be predicted well and it doesn't take more than at most some months to factor a number.

[QUOTE=Bob Silverman]You could try ECMNET. Help find factors of 2^n+1 and 2^n-1 so we don't
waste time factoring numbers with NFS that could more easily be done with
ECM. :banana:[/QUOTE]

I just set 2 machines on it. Is there any possibility to track how many curves have been done on those numbers?
Personally, I like the ECM Server, e.g. used by ElevenSmooth. This way, ECM is completely automated. It uses gmp_ecm as well.

Do you know a project that can try to ecm 24737*2^991+1? It's the last test of Seventeen or Bust with n < 1000 for which there is no known factor...

[QUOTE=Mystwalker] Is there any possibility to track how many curves have been done on those numbers?

<snip>

Do you know a project that can try to ecm 24737*2^991+1? It's the last test of Seventeen or Bust with n < 1000 for which there is no known factor...[/QUOTE]

I gave a reference which keeps track of ECM effort on 2,n+ and 2,n-

/http://www.mersenne.org/ecm.htm

Please report any ECM efforts you might make to George Woltman (you can
email him from the GIMPS website).

I know of no project to factor your suggested number; IMO there are already
too many such projects. The Cunningham project has been going on for
over 80 years. It is always easy to start up a project to factor some new
set of numbers. One always makes easy early progress. But (IMO) the real
pleasure comes from factoring a (set of) numbers that has withstood efforts
for a long time. Such as finishing 2,n+ and 2,n- to n=1200.

[QUOTE=Unregistered]Zetagrid will probably go down after January[/QUOTE]

Why is that? Do you think they will stop after they reach 1 trillion zeroes?