20091022, 19:42  #1 
Aug 2005
Seattle, WA
2×3^{4}×11 Posts 
Strange timing for GMPECM 6.2.3
Can anybody explain the following anomaly, seen in GMPECM 6.2.3?
Code:
% echo 187916912042724004738494596691073958201795717624345429344224699255786723101372929902219413902513323285241  ecm sigma 3455028177 3e6 GMPECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 187916912042724004738494596691073958201795717624345429344224699255786723101372929902219413902513323285241 (105 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3455028177 Step 1 took 9263ms Step 2 took 4948ms ********** Factor found in step 2: 211523074369177100475152901773214226961 Found probable prime factor of 39 digits: 211523074369177100475152901773214226961 Probable prime cofactor 888399114863220054416373993221092999905502700297301957333000997481 has 66 digits Code:
% echo 211523074369177100475152901773214226961  ecm sigma 3455028177 2e5 GMPECM 6.2.3 [powered by GMP 4.3.1] [ECM] Input number is 211523074369177100475152901773214226961 (39 digits) Using B1=200000, B2=128954290, polynomial Dickson(3), sigma=3455028177 Step 1 took 12669ms Step 2 took 1052ms I have seen this with several other small input numbers, all in the 3640 digit range. What the heck is ecm doing for those 12 seconds? 
20091022, 21:12  #2 
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
2·5·7·61 Posts 
Why are you trying to run ECM on a prime? No wonder it's being wacky...
besides, I'm pretty sure that you'd find nothing at all, or the prime you're trying to ECM. 
20091022, 21:48  #3  
Aug 2005
Seattle, WA
2×3^{4}×11 Posts 
Quote:
Come to think of it, when I ran 'make check' all the tests passed, but some of them looked like they were taking way too long. I guess that's another example of the problem. 

20091022, 22:24  #4  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
1000010101110_{2} Posts 
Quote:
Code:
C:\Files\Prime\aliquot\ecm>ecm sigma 3455028177 3000000 GMPECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM] 211523074369177100475152901773214226961 Input number is 211523074369177100475152901773214226961 (39 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3455028177 Step 1 took 8500ms Step 2 took 6047ms ********** Factor found in step 2: 211523074369177100475152901773214226961 Found input number N 1879169120427240047384945966910739582017957176243454293442246992557867231013729299022194139025133232 85241 Input number is 187916912042724004738494596691073958201795717624345429344224699255786723101372929902 219413902513323285241 (105 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3455028177 Step 1 took 23703ms Step 2 took 15328ms ********** Factor found in step 2: 211523074369177100475152901773214226961 Found probable prime factor of 39 digits: 211523074369177100475152901773214226961 Probable prime cofactor 888399114863220054416373993221092999905502700297301957333000997481 has 66 di gits By the way, here's the best B1 and B2 to find this particular factor with this particular sigma: Code:
C:\Files\Prime\aliquot\ecm>ecm sigma 3455028177 1961957 18910769 GMPECM 6.2.3 [powered by GMP 4.2.1_MPIR_1.1.1] [ECM] 211523074369177100475152901773214226961 Input number is 211523074369177100475152901773214226961 (39 digits) Using B1=1961957, B2=22231452, polynomial x^2, sigma=3455028177 Step 1 took 5297ms Step 2 took 188ms ********** Factor found in step 2: 211523074369177100475152901773214226961 Found input number N 

20091023, 21:12  #5 
Aug 2005
Seattle, WA
2·3^{4}·11 Posts 
Ah, that's a good data point to know. Thanks. So it sounds like something in my particular build could be the problem. Akruppa, if you're out there, any advice on how to go about tracking this down? In particular, how can I figure out what ecm is doing for such a long time?
Oh yes, I tried it several times. Besides, you can look at my paste of output above and note that even for a ridiculously low B1 like 2e5, it still took longer than running the full B1 of 3e6 on the much larger composite number. Something is clearly wrong. 
20100210, 14:01  #6  
"Nancy"
Aug 2002
Alexandria
100110100011_{2} Posts 
Quote:
Alex 

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