20121125, 16:17  #45 
"James Heinrich"
May 2004
exNorthern Ontario
2×5^{2}×7×11 Posts 
As I'm working slowly through the ranges I'm starting to see some odd behaviour. Specifically, some ranges (of 10million exponents) are finding approximately 15000 factors but other close ranges are only finding about half of that. For example:
Code:
Range Candidates Factored Unfactored Factors in 20000<k<100000 2130M 464,860 156,532 308,328 15,644 2140M 465,831 154,327 311,504 13,301 2150M 465,334 147,582 317,752 7,336 2160M 465,180 147,187 317,993 7,204 Code:
Range Candidates Factored Unfactored Factors in 20000<k<100000 1050M 481,207 169,206 312,001 16,183 1060M 481,433 164,587 316,846 16,218 1070M 480,645 164,706 315,939 16,263 1080M 481,153 164,910 316,243 16,275 1590M 471,866 160,013 311,853 15,984 1600M 471,784 159,748 312,036 16,124 1610M 471,178 159,317 311,861 15,697 1620M 471,758 159,554 312,204 15,660 edit: the dropoffs are visible in the graph, notably the sharp drop around 2140M as noted above. Last fiddled with by James Heinrich on 20121125 at 16:39 Reason: fixed: ranges are 10million, not 1million 
20121125, 16:57  #46  
Jun 2003
5,407 Posts 
Quote:
Last fiddled with by axn on 20121125 at 16:59 

20121125, 18:22  #47  
"James Heinrich"
May 2004
exNorthern Ontario
111100001010_{2} Posts 
Quote:
As one check, I ran through 100 exponents at 2150M (that had been declared nofactor up to k=99999 by PARI) using mfaktc up to 2^65. I did find one small factor in that range that should have been caught, but for some reason was not. Unfortunately I've deleted the source file that was used to generate that range, but I'm recreating it now... <sudden flash of realization> :surprised I think I may know the source of the problem... as stated elsewhere I'm using PHP to generate the PARI code, and I've moved the selection of jumplist from PARI code to the PHP generating code for a little runtime speedup. Unfortunately, the PHP installation on my server is 32bit and so when I'm checking p%60 that is where failure enters the scene. For example, the missed factor I found with mfaktc in my test above (M2,150,001,863) should have 2,150,001,863 mod 60 = 23. To get real weird, PHP can fail in 2 different ways: Code:
echo ('2150001863' % 60); = 7 echo (2150001863 % 60); = 53 Fortunately the gmp_mod function is available and will work correctly on any size exponent. So now I can regenerate all the work above 2^31. So none of the generated factors above 2^31 were wrong, but about half of the factors were missed. Thanks axn for the kick in the right direction. 

20121126, 01:38  #48 
Romulan Interpreter
"name field"
Jun 2011
Thailand
23622_{8} Posts 
If you use some code related to the one in post #37 (with 60 classes split) then you may not use the right starting value for k? (multiple of 60? 20000 is not multiple of 60, you have to start with 19980, or rotate the vectors accordingly) (also just a guess).
edit: sorry, did not see your last post, I posted after axn's post (strange, the forum breaks the page at post #46, and I see post #47 as a new page, I am sure I selected 25 posts on page...) Last fiddled with by LaurV on 20121126 at 01:44 
20121126, 01:44  #49 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 

20121126, 01:53  #50  
"James Heinrich"
May 2004
exNorthern Ontario
F0A_{16} Posts 
Quote:
But I've now regenerated my assignment files and it seems to be happily finding all the factors it was missing before, so I'm happy. 

20130102, 03:25  #51  
"James Heinrich"
May 2004
exNorthern Ontario
111100001010_{2} Posts 
Quote:
My two predictions were remarkably accurate. Today is 40 days after I posted that, and I found 5,099,114 factors using this method. (disclaimer: that doesn't mean quite that many candidates were eliminated; those "extra" 100k factors probably accounts for the cases where multiple factors were found for k<100000) Thanks again to everyone who helped me figure out this code. 

20140411, 10:07  #52 
Romulan Interpreter
"name field"
Jun 2011
Thailand
10130_{10} Posts 
Sorry that I am waking up this topic. I searched for it in the light of this new discussion, I did not get the right thing I was searching for, but reaching this topic remembers me that I had implemented the "420 classes" not long after this discussion, doing a pari script to generate the vectors. The code might be useful to somebody, so I will include here. It is about 15% faster than the "60 classes" code described in the posts above. It also eliminates the restriction that the starting q be a multiple of 420. The version with 4620 classes would be slower because of overhead (hey! pari is not mfaktc!).
Somebody can use it for understanding how mfaktc works, or for TFin small exponents which are outside of the mfaktc range (again, there are much faster programs there outside, this is not for "production" purposes). tf420.gp.txt [can't insert code, is over 10k characters limit] Last fiddled with by LaurV on 20140411 at 10:14 
20140411, 11:00  #53 
"James Heinrich"
May 2004
exNorthern Ontario
2×5^{2}×7×11 Posts 
Naysayers suitably ignored...
Thanks for your updated code. Yes, I'm still using your 60class version even as I type this (taking 2000M4000M from 2^{51} to 2^{52}). I'll go regenerate my assignment files with the 420class version  thanks! 
20140423, 20:10  #54 
"Forget I exist"
Jul 2009
Dumbassville
3×2,801 Posts 
same question for double mersenne numbers ?
I know that the form 2*k*p+1 stays the same for p=2^q1; but if I form MMq into 2*j*(2*l*q+1)+1 the k value for this becomes:
Code:
(2*l + 1/q)*j converting the k value to: Code:
(2*q*l + 1)*x Code:
(2*q*l + 1)*x + l is there anything else that should be said about this value. Last fiddled with by science_man_88 on 20140423 at 20:41 
20140423, 21:57  #55 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
26D6_{16} Posts 

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