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Old 2011-04-04, 16:37   #1
xilman
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Default Factoring GCW numbers - call for assistance.

I've been factoring Cullen, Woodall and their higher-base counterparts for rather a long time now, ably assisted by a good number of other people, some of whom are stalwarts of Mersenne Forum.

Cullen numbers, C(n) are n*2^n+1 and Woodall numbers are n*2^n-1. My project also uses values between 3 and 12 inclusive for the base instead of 2. The starting URL is http://www.leyland.vispa.com/numth/f...oodall/cw.html

A V2 ECMnet server is running on 83.217.167.177:8194 --- this is the one which had 12 thousand composites in its ecmserver.ini file which Mark Rodenkirch loaded into the V3 server he is developing. As of a few hours ago the server was modified to allocate tasks for which no factor is known. In consequence, there are now only 110 composites in its database. These numbers, along with the smallest composites (currently at c130) and those easiest by SNFS (currently at difficulty 180 digits or so) are my Most Wanted Numbers.

If anyone would like to point an ECMnet client at my server I would be very grateful. Tasks are currently being allocated at the B1=1M level (optimal for 35-digit factors) but that will change to 3M in the next day or so. For those who like to see instant results, the tasks being allocated are amongst the easiest I know of within the population of ECMnet servers.


Paul

Last fiddled with by xilman on 2012-08-14 at 20:06 Reason: Fix link to current target.
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Old 2011-04-04, 17:43   #2
jyb
 
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Paul, I can't seem to get this server to respond to any requests for work. Is it working for you locally? (For reference, the server completes the TCP handshake but then fails to respond to any further traffic of any sort.)
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Old 2011-04-04, 17:44   #3
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For those of us without ECMNet clients, where do we get the latest and greatest binaries/source to use?
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Old 2011-04-04, 17:49   #4
Batalov
 
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Code:
[2011-04-04 17:46:25 GMT] GCW: GetWork error.  Nothing returned by server.
[2011-04-04 17:46:28 GMT] GCW: Getting work from server 83.217.167.177 at port 8194
[2011-04-04 17:46:39 GMT] GCW: GetWork error.  Nothing returned by server.
[2011-04-04 17:46:39 GMT] GCW: Getting work from server 83.217.167.177 at port 8194
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Old 2011-04-04, 18:01   #5
xilman
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Quote:
Originally Posted by Jeff Gilchrist View Post
For those of us without ECMNet clients, where do we get the latest and greatest binaries/source to use?
Mark's home page is a good place to start: http://home.roadrunner.com/~mrodenki...me/ECMNet.html

Paul
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Old 2011-04-04, 18:10   #6
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Quote:
Originally Posted by jyb View Post
Paul, I can't seem to get this server to respond to any requests for work. Is it working for you locally? (For reference, the server completes the TCP handshake but then fails to respond to any further traffic of any sort.)
yes, it is working locally and at least two external sites can connect (admittedly, one of them is under my control). However, the server might be having problems as indicated by this snippet from the log file:
Code:
[2011-04-04 16:55:58 GMT] lionel_debroux@yahoo.fr (mbp) at 109.213.129.115: Sent GC_10_943_C946 : 307 ECM curves with B1=1000000
[2011-04-04 16:56:04 GMT] lionel_debroux@yahoo.fr (actinium) at 109.213.129.115: Sent GC_10_943_C946 : 307 ECM curves with B1=1000000
[2011-04-04 16:56:14 GMT] paul@leyland.vispa.com (mesh_2:v2.0k) at 192.168.1.66: Received GW_7_962_C816 : 4 ECM curves with B1=1000000
[2011-04-04 16:56:15 GMT] paul@leyland.vispa.com (mesh_2:v2.0k) at 192.168.1.66: Sent GW_11_500_C524 : 306 ECM curves with B1=1000000
[2011-04-04 16:56:15 GMT] Total Time:  1:40:43  Curves: 708  Total Work: 368744  Total Factors Found: 0
[2011-04-04 16:57:43 GMT] Dropped connection due to missing 'FROM' identfier.
[2011-04-04 16:57:43 GMT] pcl@anubis (anubis4) at 192.168.1.3: Received GC_10_943_C946 : 2 ECM curves with B1=1000000
[2011-04-04 16:57:43 GMT] Total Time:  1:42:11  Curves: 710  Total Work: 370533 Total Factors Found: 0
[2011-04-04 16:57:43 GMT] Pipe Interrupt with code 13.  Processing will continue
[2011-04-04 16:57:43 GMT] Error sending </table> to localhost:8194
[2011-04-04 16:57:43 GMT] Pipe Interrupt with code 13.  Processing will continue
[2011-04-04 16:57:43 GMT] Error sending <table frame=box align=center border=1> to localhost:8194
[2011-04-04 16:57:43 GMT] Pipe Interrupt with code 13.  Processing will continue
[2011-04-04 16:57:43 GMT] Error sending <tr><td>B1<td><b>ECM Curves<td><b>P_1 Tests<td><b>P-1 Tests</tr> to localhost:8194
[2011-04-04 16:57:43 GMT] Pipe Interrupt with code 13.  Processing will continue
[2011-04-04 16:57:43 GMT] Error sending <tr><td>2000<td>522<td>3<td>1</tr>  to localhost:8194
[2011-04-04 16:57:43 GMT] Pipe Interrupt with code 13.  Processing will continue
[2011-04-04 16:57:43 GMT] Error sending <tr><td>50000<td>300<td>3<td>1</tr>
 to localhost:8194
The French site is one which connected successfully. Another looks like it wasn't configured correctly. "mesh" and "anubis" are local machines.

Part of Mark's re-write is to make the server more robust against error conditions.

Anyway, I've restarted the server in the hope that it will behave better.

Paul
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Old 2011-04-04, 18:22   #7
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Quote:
Originally Posted by xilman View Post
Anyway, I've restarted the server in the hope that it will behave better.

Paul
Thanks, that seems to have done the trick.
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Old 2011-04-05, 05:37   #8
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Yes, my computers managed to connect to the server before it hung. The server hung again a bit later, but I guess you restarted it again.
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Old 2011-04-05, 08:40   #9
xilman
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We have our first success!

Code:
[2011-04-05 00:21:07 GMT] GW_11_902_C943: probable factor returned by becker(a)cs.stanford.edu (GCW8)!  Factor=169216071936589830635038351509212921  Method=ECM  B1=1000000  Sigma=2101580435
[2011-04-05 00:21:07 GMT] GW_11_902_C943: Composite factor returned by becker(a)cs.stanford.edu (GCW8)!  Factor=11560242405034094596309119556941604157705796462098010672133329157398179133732742986435730684643607362822046458222090383540737930368133539670029762628168201166499145047416084333018134640033429231563054792383075863294957083533472714880314340180352069455893858891557480677511383860802589634019431578970435296218193409271489330792154643607628864241136145937778061748953297604816434904091761527843808084032623147801547027634435021555061768259542524468072023645639008247790039736184913622605871613315977358826290866059514473585956685707052086469154607481326228330845838356212736394385079353533340849529709970531985692295366119019645116872213280833086412661585099547067057693694235486351829391697768164715746029814151730550800983668912263003113940179878247222800192178620529350834088529588823250413478216521502839482096375025334160727273813434666296304316572538212418286064067864405270536265270710408751792216009821  Method=ECM  B1=1000000  Sigma=2101580435
A p36 if my counting is accurate.

Paul
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Old 2011-04-06, 08:55   #10
xilman
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The page at http://www.leyland.vispa.com/numth/f...oodall/gcw.htm and the tables it references have all been updated.

In particular, the rotcafs found by Jon Becker and Serge Batalov are both recorded.

Thanks for your assistance!

Paul
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Old 2011-04-08, 21:58   #11
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Quote:
Originally Posted by xilman View Post
Cullen numbers, C(n) are n*2^n+1 and Woodall numbers are n*2^n-1. My project also uses values between 3 and 12 inclusive for the base instead of 2. The starting URL is http://www.leyland.vispa.com/numth/f...oodall/gcw.htm
The file algebraic.txt there says "It is possible, indeed probable, that some algebraic factorizations have been missed". This seems odd, since the two known kinds of algebraic factorizations (cyclotomic and Aurifeuillian) are easy to check, and unknown kinds are unlikely to exist. Anyway, I did find some that apparently were missed: GW(3,384) and GC(3,384) (because 384*3^384=(2*3^55)^7), GW(4,250) and GC(4,250) (because 250*4^250=(5*2^167)^3), and GC(4,625) (because 625*4^625=4*(5*2^312)^4). All of these numbers have already been completely factored, though, so this doesn't really help very much.
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