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. 
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[/CODE] 
A question for you.
This number: [URL]http://factordb.com/index.php?query=2%5E4096%2B1[/URL] 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. [URL]http://factordb.com/index.php?query=376322477048617706282462388956027634343218845103390837212250702240959281150975236858250674636956552977575644992330996492338135918917204224925730238170019337820662498693330214493679906249430900443624368413333595681442733617839085943481006048777973773591406068191894247135076070607701671255689393354833931428904840400137034536160570869727614264736511398659942277301367066020633087558665671166875762563942035532792180363929088374279589503341188047214073086726851135261749578902508394601821973454790627006430017331868404601460469312723942289592524483574675347884177907988641059081276472500778218279942489601992074842988131294457842242038301712355434936375127073908356537956356729529445349120612641176599142068049970365809774454799542388248241553661260847138183261484650763885768211561752754874815731734124473715998503717723148675023907224588066094282547359309526247271656601476531496818804530635931377069937447283246131305098070657511838862477777176956021954715464471389371275116614094336106603451173330189453927144813866143757504892797659528403039717804532780633926183197591614987388529999585227478353262018919671[/URL] 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. 
It is not related.
It is a cofactor of (2^4096+1)/25860116183332395113497853167940236083358054\ 650286886725246241569916604094012679963198712829716480001[COLOR="Red"]2[/COLOR] not of 2^4096+1 
ans = 10906594903029791068395400811884464627409515459009973450004302442452725255227
P35 = 62611614700115894971255725399191227 P42 = 174194435892891975029270196982744708432001 
Very long factor(s), good catch. Do you plan to report them to mersenne.org ?

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! 
If you are reporting a bug, please list the YAFU version number, and the composite & result so someone else can try to reproduce it.

[QUOTE=storflyt32;385008]ans = 10906594903029791068395400811884464627409515459009973450004302442452725255227
P35 = 62611614700115894971255725399191227 P42 = 174194435892891975029270196982744708432001[/QUOTE] What is this number, anyway? 
ans = 5687625641025641025641025641025641025641025641025641025641025641025641025641
P33 = 213843479182611070647190753814939 P44 = 26597143213184949293331777384754973697286219 
I *guess* he is factoring the "smallest composite without known factors" from the factordb, those are also 76 digits.

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