20040915, 13:29  #1 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 
Nice Result! M971
In case everyone has not yet heard:
David Symcox factored M971 using Mprime. This was the smallest Mersenne number with no known factors. He found a 53 digit factor with ECM and the cofactor was prime. This again shows that factors remain to be found of 2^n+1 and 2^n1 for n < 1200. This is a useful pursuit for those with slower machines who do not want to wait many months for a single LL test. See: http://www.mersenne.org/ecm.htm Bob 
20040916, 13:50  #2 
Aug 2002
Termonfeckin, IE
AD0_{16} Posts 
OK! So I'm intrigued and want to run some ECM tests on the 2+ Cunningham tables. I have a P4 with wondows and another with linux  both reasonably fast machines. Should I use mprime or gmpecm? I am very familiar with mprime/prime95 whereas gmpecm would require a bit of learning. Moreover, I understand that on P4s P95/mprime is faster. But is that only that case for number of the form 2^n1 or also for 2^n+1? The machines have about 200MB of free memory that can be devoted to GMPECM. The number I am looking at is 2^1033+1 which hasn't had any ECM done even for the 40 digit level.

20040916, 14:13  #3 
P90 years forever!
Aug 2002
Yeehaw, FL
2^{2}×43×47 Posts 
You are probably better off running GMPECM

20040916, 14:15  #4  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
3×17×227 Posts 
Quote:
Good luck! Paul 

20040916, 14:43  #5  
Mar 2003
New Zealand
2205_{8} Posts 
Quote:
2^10331 and 2^1033+1 can be tested simultaneously by running curves on 2^20661. (on a P4 with Prime95 it is much faster to test 2^20661 than 2^1033+1, and so you effectively get to test 2^10331 for free). 2^10331, 2^1033+1, 2,2066L and 2,2066M (these last two are factors of 2^2066+1, also in the Cunningham tables) can all be tested simultaneously by running curves on 2^41321. All four numbers have reasonably large unfactored parts, all above 250 digits, so while gmpecm would be faster than Prime95 on the stage 2 step, it is not as big a difference as for some other numbers. If you wanted to keep things simple and just use Prime95, 2^20661 or 2^41321 would be good choices I think. All four numbers have had a similar level of ECM effort reported too, i.e. tested to 40 digits. 

20040916, 14:54  #6 
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Here are other exponents where both 2^n+1 and 2^n1 are not completely factored:
787, 799, 823, 853, 859, 887, 893, 905, 913, 923, 947, 949, 961, 991, 1001, 1009, 1019, 1021, 1025, 1027, 1033, 1037, 1043, 1051, 1055, 1067, 1079, 1087, 1091, 1105, 1109, 1115, 1123, 1127, 1129, 1133, 1135, 1139, 1147, 1151, 1153, 1157, 1159, 1161, 1163, 1165, 1167, 1175, 1177, 1183, 1187, 1191, 1193 As for using gmpecm, the best you can do is try out and take timings. If you have an Athlon sitting somewhere, doing stage 1 with Prime95 on P4 and stage 2 with gmpecm on Athlon would be ideal. If you do stage 1 on two (or more) numbers simultaneously, you should split the residue modulo the individual numbers before feeing it to gmpecm. It saves both time and memory. The thread http://www.mersenneforum.org/showthread.php?t=2326 has more info. Alex 
20040916, 14:58  #7  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×937 Posts 
Quote:
on step 1 and GMPECM on step 2. Mprime can output the result of Step 1. GMPECM can accept it for step 2. 

20040916, 15:05  #8  
"Bob Silverman"
Nov 2003
North of Boston
2^{3}·937 Posts 
Quote:
tested through 40 digits, while for the corresponding 2^n+1, many have not been fully tested at this level.. It would be somewhat wastefull to test both at the 40 digit level. OTOH, very FEW of these have been fully tested to 45 digits. Thanks for helping out. Bob 

20040916, 15:21  #9 
"Nancy"
Aug 2002
Alexandria
100110100011_{2} Posts 
I think it's permissible to skip B1=3M for one of the numbers. Even if a ~p40 exists, the expected time to find it with B1=11M is not that much higher than with B1=3M, and the time saved by doing both numbers at once should more than make up for that.
Alex 
20040916, 15:21  #10 
Aug 2002
Termonfeckin, IE
2^{4}×173 Posts 
Okay! Looks like I will do stage 1 on 2^41321 using Prime95 on a P4 followed by splitting up the residues and feeding them to gmpecp on my Athlon machine for stage 2.
Now a few questions: 1) Are there Windows binaries for gmpecm on an Athlon? 2) Does anyone keep track of ECM done on LM numbers? 3) Now this may be a very silly question to ask but is there any sense at all in attempting P1 on 2^41321? 4) Can someone give a short two line desciption of what stages 1 and 2 are in ECM. I know what they are in P1. Thanks 
20040916, 15:22  #11  
P90 years forever!
Aug 2002
Yeehaw, FL
2^{2}×43×47 Posts 
Quote:


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