20110115, 16:33  #67  
"Tapio Rajala"
Feb 2010
Finland
315_{10} Posts 
Quote:
Quote:


20110115, 23:39  #68  
Jun 2003
1169_{10} Posts 
Quote:
Code:
$ echo "25320591696138535897675469195834877349466521"  ecm c 0 pp1 60000 GMPECM 6.2 [powered by GMP 4.2.2] [P+1] Input number is 25320591696138535897675469195834877349466521 (44 digits) Using B1=60000, B2=19419970, polynomial x^1, x0=2552205880 Step 1 took 88ms Step 2 took 96ms Run 2 out of 0: Using B1=60000, B2=19419970, polynomial x^1, x0=1936717407 Step 1 took 80ms [factor found by P1] ********** Factor found in step 2: 857285347808257713679 Found probable prime factor of 21 digits: 857285347808257713679 Probable prime cofactor 29535780310340488803799 has 23 digits $ 

20110116, 19:22  #69 
Jan 2011
Cincinnati, OH
2^{2}·5^{2} Posts 
Just wanted to thank lorgix, Mr. P1, and rajula for responding, and getting me started down the path of understanding, as I'm not a mathematician. I'm sure I'll have lots more questions.
Doug 
20110116, 23:13  #70  
Jun 2003
10010010001_{2} Posts 
Quote:
The quickest way to prove these numbers composite would be a PrP test, which wouldn't tell us the prime factors. In practice, we don't bother, because we're interested in the prime factors anyway, and factoring them is so easy. Theoretically, if a large P1 factor should resist factorisation for any length of time, we might begin to suspect it to be prime after all. To prove a number of that size prime, I'd use Pari/GP's isprime() function. There are several other tools capable of proving much larger numbers prime. Last fiddled with by Mr. P1 on 20110116 at 23:13 

20110117, 09:19  #71 
Sep 2010
Scandinavia
3×5×41 Posts 
Another find thanks to Suyama's extension;
P1 found a factor in stage #2, B1=85000, B2=1742500. M2294807 has a factor: 4743377217925125644071 k= 3^3*5*751*3851*2647063  You're welcome drh! I'm learning too, heck we all are. I usually use http://factordb.com/, that site stores the factor as well. But all the other suggestions are great too. 
20110117, 18:25  #72 
Jun 2003
7·167 Posts 

20110117, 18:31  #73 
Sep 2010
Scandinavia
3×5×41 Posts 
Actually the output doesn't say.
But it always uses E=6 under similar (to the ones in question) circumstances. 
20110117, 19:44  #74 
Jan 2011
Cincinnati, OH
2^{2}·5^{2} Posts 
From TF 
M80307593 has a factor: 144625571114343550097 
20110117, 23:51  #75  
Jun 2003
10010010001_{2} Posts 
Quote:
How many relative primes out of how many were you able to do per pass? 

20110118, 08:07  #76 
Sep 2010
Scandinavia
3×5×41 Posts 
All 480 in one pass. 498MB.
I used to think the same. But it appears to me now that it doesn't do that if a factor is found. More recent find below, where Suyama's extension wasn't needed. Still used E=6, but doesn't show it here for some reason. P1 found a factor in stage #2, B1=90000, B2=1755000. M2299571 has a factor: 103653914718894079697 
20110118, 08:12  #77 
Sep 2010
Scandinavia
3×5×41 Posts 
Close or what?
P1 found a factor in stage #2, B1=95000, B2=1947500. M2444359 has a factor: 1588994437060952149274017 k= 2^4*3*31*41*197*13901*1945487 
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