20090112, 04:27  #1 
Mar 2006
11×43 Posts 
Lucky gmpecm curve...
I just found a 41 digit factor using a B1=1e6! I was hoping it might make it onto the Top list for 2009, but I see the last entry is already at 42 digits. Oh well, Just wanted to share with everyone.
Has anyone else had a lucky curve, where you found a factor that is "many" digits above what was expected? echo "10^1218363"  ./ecm sigma 242376148 1000000 GMPECM 6.1.2 [powered by GMP 4.2.1] [ECM] Input number is 10^1218363 (121 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=242376148 Step 1 took 13469ms Step 2 took 7797ms ********** Factor found in step 2: 57315926928065111052544509749282072073751 Found probable prime factor of 41 digits: 57315926928065111052544509749282072073751 Composite cofactor (10^1218363)/57315926928065111052544509749282072073751 has 81 digits 
20090112, 05:22  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,421 Posts 
The probability of a p41 with 904 B1=1e6 curves is ~0.1. Not very rare.
If the c81 splits p41.p41, then I'd say you had something (a 3brilliant split). Ah. Alas, no... Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=161802477 Step 1 took 1828ms ********** Factor found in step 1: 1766409430355415794746950731 Found probable prime factor of 28 digits: 1766409430355415794746950731 Probable prime cofactor ((10^1218363)/57315926928065111052544509749282072073751)/1766409430355415794746950731 has 53 digits 
20090112, 08:26  #3  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2·5·587 Posts 
Quote:


20090112, 13:05  #4 
Mar 2006
11×43 Posts 
Because I have made additions to it that are useful in my search for brilliant numbers. I actually call my binary 6.1.2.1. But I haven't changed the version number that is output by the program, so 6.1.2 is what shows up.
I should probably diff this against 6.2.1, and see if it will apply cleanly. I made modifications to 6.0.1, and reimplemented those in 6.1, and then reimplented those in 6.1.2. (back before I knew a tool like diff existed, still not sure if it'll work) I didn't know how fast gmpecm was going to keep getting updates, so I just stopped at 6.1.2 since it worked well for me. 
20090112, 16:29  #5 
Apr 2007
Spessart/Germany
2×3^{4} Posts 
Hello,
this is a curve 11 digits above the nominal size of 30 digits: Code:
(08/12/25) GMPECM 6.1.3 [powered by GMP 4.2.2] [ECM] Input number is ((367#)+((397#)/(367#)))/854170501969645699246152769 (122 digits) Using B1=250000, B2=128992510, polynomial Dickson(3), sigma=280297040 Step 1 took 3235ms Step 2 took 1687ms ********** Factor found in step 2: 12277223854594410567719074755920634852313 Found probable prime factor of 41 digits: 12277223854594410567719074755920634852313 Probable prime cofactor (((367#)+((397#)/(367#)))/854170501969645699246152769)/12277223854594410567719074755920634852313 has 82 digits Matthias 
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