20140615, 03:23  #1 
Feb 2013
2·229 Posts 
Didn't even find a useless factor of an uninteresting number! Take that!
10^444031*91 has a known factor 66666323.
Apparently there is a factor 114851129 of (10^444031*91)/66666323 as well. It took quite a bit of time finding this small factor using Yafu's ECM command and for now I did not redirect the output to any file. Therefore the whole process including the comparison of the numbers became more or less manual between three different DOS window boxes. Last fiddled with by storflyt32 on 20140615 at 03:25 Reason: Better wording. 
20140615, 04:37  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3·5·313 Posts 
It takes only a few seconds to find by this (very slow) script:
Code:
> gp q ? p=66666321; ? while(1,p=nextprime(p+1);if(Mod(10,p)^444031*9==1, print(p))) 66666323 114851129 
20141008, 01:39  #3 
Feb 2013
2×229 Posts 
A question for you.
This number: http://factordb.com/index.php?query=2%5E4096%2B1 The composite number there (a C1133) has not been factored. I know that there have been made several attempts, but for now without success. Another number more indirectly related to this number is being found here. http://factordb.com/index.php?query=...53262018919671 Perhaps I should rather tell you that I do have a factor for this number lying around. It is a somewhat larger factor, a P34, to be more precise. I will need to carry out the factorization once again, because I have lost it. For now I only do have the mentioned factor available. 
20141008, 02:07  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2·3·5·313 Posts 
It is not related.
It is a cofactor of (2^4096+1)/25860116183332395113497853167940236083358054\ 6502868867252462415699166040940126799631987128297164800012 not of 2^4096+1 
20141012, 06:16  #5 
Feb 2013
2×229 Posts 
ans = 10906594903029791068395400811884464627409515459009973450004302442452725255227
P35 = 62611614700115894971255725399191227 P42 = 174194435892891975029270196982744708432001 
20141012, 08:58  #6 
Feb 2010
Sweden
173 Posts 
Very long factor(s), good catch. Do you plan to report them to mersenne.org ?

20141013, 14:52  #7 
Feb 2013
2×229 Posts 
Thanks!
Anyway, I notice a problem with the Yafu factoring software. I am having a 64bit computer, so I am using both the 32bits and 64bits versions of this software. Apparently the 32bit version is returning the wrong cofactor number in the result. This has now become a very annoying feature and needs to be fixed as soon as possible. Thanks again! Last fiddled with by storflyt32 on 20141013 at 14:54 
20141013, 17:22  #8 
"Curtis"
Feb 2005
Riverside, CA
3·1,579 Posts 
If you are reporting a bug, please list the YAFU version number, and the composite & result so someone else can try to reproduce it.

20141013, 17:26  #9 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×3×5×313 Posts 

20141014, 13:10  #10 
Feb 2013
2·229 Posts 
ans = 5687625641025641025641025641025641025641025641025641025641025641025641025641
P33 = 213843479182611070647190753814939 P44 = 26597143213184949293331777384754973697286219 
20141014, 23:33  #11 
"Victor de Hollander"
Aug 2011
the Netherlands
2^{3}×3×7^{2} Posts 
I *guess* he is factoring the "smallest composite without known factors" from the factordb, those are also 76 digits.

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