Update 2013-07-04
 

I see it's rather a long time --- not since April in fact --- without a status update here. Apart from the information about the yoyo@home BOINC effort that is. The [URL="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.html"]web site[/URL] was last updated at the end of 2013Q2, or 30 June. At that time 9990 numbers had been fully factored and 12036 composites remained to be done.

In that two months, both yoyo@home and Rob Hooft have found many ECM factors independently of the ECMnet server running at 83.217.167.177:8194. Several people have been connecting their clients to that server, including Jeff Gilchrist, Pierre Jammes, Mathew Steine, Ralf Recker, Rocke Verser and myself. Apologies if I've inadvertently omitted anyone else.

Phil Frakes, Jo Yeong Uk and I have been clearing out quite a few composites with NFS.

A few results have accumulated in the first week of July. Another SNFS is due to finish here later today; when it has been processed I'll update the web page.


The result of all this effort is that we are now certain to reach ten thousand fully factored numbers and extremely likely to reduce the number of composites below twelve thousand before the end of the year. Both the composites with under 150 digits are in progress and only one SNFS candidate is easier than 211 digits. Targets for the end of the year may be to clear out all C15x composites by GNFS and all SNFS candidates below 220 digits. Reaching either of these is likely to prove difficult. Achieving both of them is likely to be impossible without significantly greater contributions. I would love to be proved wrong.

Again, my thanks to everyone who has contributed and continues to contribute.


Paul

[QUOTE=xilman;345233]
The result of all this effort is that we are now certain to reach ten thousand fully factored numbers and extremely likely to reduce the number of composites below twelve thousand before the end of the year.[/QUOTE]Each of these target has now been achieved. The [URL="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.html"]update just posted[/URL] shows 10029 fully factored GCWs. The 12K target fell yesterday when three more SNFS results were reported --- two by NFS@Home and one by me. There are now 11997 remaining composites. It doesn't seem so long ago that the number dropped below 15K...

Once more, my thanks to all the contributors, whether by NFS or ECM; whether by individuals or parts of teams like NFS@Home and ECMnet clients.

Paul

End of Q3
 

The third quarter of 2013 has just finished and the [URL="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/2013q3.txt"]corresponding progress file[/URL] contains 253 factorizations found by a large number of contributors.

There is now a total of 20909 factors reported since the extended project was restarted in 2000. It seems very likely that we'll reach the 21K millstone by the end of the year, especially as ten factors have already been reported in the first three days of the current quarter.

The V2 ECMNET server is still running at 83.217.167.177:8194 for anyone who would like a fire&forget approach to factoring the GCW numbers. Working with Mark Rodenkirch and Tim Charron, I have set up an experimental V3 server on an as-yet inaccessible machine. It is loaded with the GW(9,x) table and two factorizations have already been discovered in the last few days,

If there are any [strike]members of the lunatic fringe[/strike] public-spirited pioneers who would like to help me debug the V3 server, please email me and I'll open up port 8195 on the firewall. The server accepts both V2 and V3 clients but a better experience is obtainable with V3 clients. If you need help setting up V3 I'll do what I can.

Paul

October 2013
 

A total of 79 GCW factors were reported in October. The bulk of them were found by Rob Hooft, who is running ECM, and NFS@Home and their post-processing assistants. Several individuals ran NFS of one flavour or another, including Sean Wellman, Tom Womack and me. ECM factors were also found by Sean, Geoff Gilchrist, yoyo@home and me. A number of others have been searching (so far in vain) with ECM; they should get lucky soon enough and their efforts are appreciated despite their recent lack of factors.

Strangely enough, there has been a drought of factors from the ECMNET clients connecting to either server. Doubtless Poisson is being coy with his statistics again.

At the end of the month a total of 20977 factors had been discovered since I first made the tables public in September 2000 and a total of 10162 GCW numbers had been fully factored. There wre 11859 composite cofactors remaining, of which the smallest has 151 digits and the easiest still available for SNFS has difficulty 216. Fuller details are at [URL="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.html"]the usual place[/URL].

The most wanted number remainsW951_C290 --- the only remaining base-2 number without any known factors. In the last day or two (so not strictly a report for October) Greg Childers has been running step 1 at 260M of around a thousand curves on GPUs and I'm running step 2 here on spare CPU capacity. Six hundred curves have completed. Needless to say, no factors have yet appeared.

All your contributions are very welcome. Please feel free to contact me by whatever means if you would like to reserve numbers or would like assistance with the software.


Thanks!

Paul

Wow!
 

I should post a more general update but this one can't wait.

Until a few minutes ago, 3,451+ was a 216-digit composite. Over an hour ago, this appeared:
[code]found factor: 811696958388624812149474162447939183387298383116311023122025573609990382533265355838960752467711097396619
reading relations for dependency 2
[/code]so, I thought, a three-way split. Unusual but not too uncommon.

I returned to the machine a few minutes ago to find:
[code]

found factor: 1181197284427724772711375813980165954572823959965968077
reading relations for dependency 3
read 2947701 cycles
cycles contain 9102044 unique relations
read 9102044 relations
multiplying 9102044 relations
multiply complete, coefficients have about 308.09 million bits
initial square root is modulo 337511
found factor: 811696958388624812149474162447939183387298383116311023122025573609990382533265355838960752467711097396619
reading relations for dependency 4
read 2949089 cycles
cycles contain 9104004 unique relations
read 9104004 relations
multiplying 9104004 relations
multiply complete, coefficients have about 308.16 million bits
initial square root is modulo 338411
sqrtTime: 7766
prp50 factor: 12859959525185086513945311426025999626404055469049
prp55 factor: 1181197284427724772711375813980165954572823959965968077
prp56 factor: 63118158093654069436215483522066805662546678114750688931
prp57 factor: 157430983714394251680305318042886583064897561241783003949
[/code]Not quite a 4-brilliant but pretty close! The p50 stood a fair chance of being found given the amount of ECM pre-testing but that one is only barely an ECM miss if at all. The other three would not be expected to have been found.

Paul

[QUOTE=xilman;364820]
Until a few minutes ago, 3,451+ was a 216-digit composite.
Paul[/QUOTE]

I'm confused. I thought 3,451+ was fully factored ages ago.

Extract from [url]http://www.leyland.vispa.com/numth/factorization/cunningham/3+.txt[/url]
[CODE]451 34470854184059371447414293251665361355258439. P148
[/CODE]

Edit to add

D'oh! Should have read the thread title. I now see the number is 451*3^451+1.

[QUOTE=BudgieJane;364825]I'm confused. I thought 3,451+ was fully factored ages ago.

Extract from [url]http://www.leyland.vispa.com/numth/factorization/cunningham/3+.txt[/url]
[CODE]451 34470854184059371447414293251665361355258439. P148
[/CODE]

Edit to add

D'oh! Should have read the thread title. I now see the number is 451*3^451+1.[/QUOTE]
No need to grovel. The terminology is shared with the Cunningham project for brevity, if not unambiguity.

Who wants to join me on running ecmclient to help Paul in factoring some GCW numbers? I will run it until Monday with at least 20 cores.

Attaching linux and windows 64 bit client. Only needed to edit cfg file and change email address and ID. Copy folder as many cores available.
On windows just double click on ecmclient.exe to run the client, under linux type ./ecmclient.

22 cores pointed to the server.

Found another factor but didn't receive any email notification. Is it on on your side Paul?

[QUOTE=pinhodecarlos;369679]Found another factor but didn't receive any email notification. Is it on on your side Paul?[/QUOTE]
This one?[code]
[2014-03-24 08:26:32 GMT] GW_6_728: probable factor returned by pinhodecarlos@yahoo.com (2)! Factor=3765612596073926729312275530504713031773627 Method=ECM B1=3000000 Sigma=1
[2014-03-24 08:26:32 GMT] GW_6_728: Composite factor returned by pinhodecarlos@yahoo.com (2)! Factor=29405516828076762895041226806781939419130967806736780057818608509106344102705356090934541790136839589949264818894132244030000587977580920354987937867930787219849793824430614796170674954528963643931779852115120349087327808947918986326962587939289205239311255410442610324010995520880652630986101406123087486128635546988744820532272941430982154916163189991634328431341402912488921531913470311262979913438509990097062210075263210392951536768668498065664442892344396928316013915131517344279952377054009108302910557 Method=ECM B1=3000000 Sigma=1
[/code]That is in the server's logs but mail hasn't been sent out. I will try to find out why.


Paul