20111101, 19:31  #1 
"Daniel Jackson"
May 2011
14285714285714285714
719_{10} Posts 
Program to TF Mersenne numbers with more than 1 sextillion digits?
What program can do a Trial factor on 2^{(10[sup]23}1)/9[/sup]? Is it out of Prime95's range? Is there a way to TF M(10^{100}+267)?

20111101, 22:52  #2 
Dec 2010
Monticello
5·359 Posts 
Stargate:
I think you'll run out of a few things before you can represent such numbers directly...like places to put the ones and zeros on your hard drive. These are well out of the range of any current implementations. But I suppose you could do them if you modified the source code for P95. Calculating such numbers modulo a relatively small TF should be fairly straightforward, if slow. TF simply isn't a very smart algorithm, even if it is relatively fast on a GPU. I'm curious what the significance of your choice of exponents is...and I assume 10^100+267 is known prime and has no known factors, otherwise I can factor M(10^100+267) by inspection in much less time than it takes to get P95 going. Same for your first exponent...it's got (2^231)/9 factors of 2.....unless you forgot to subtract a one somewhere!!!! 
20111101, 23:10  #3  
Jun 2003
7·167 Posts 
Quote:
Quote:
Another way to look at it is that both the time and memory required to LL test Mp is about the same as the time and memory required to TF a single (small) candidate factor of MMp, moreover different candidates could be tested in parallel on different machines. Hypothetically, a distributed computing project the size of GIMPS could make a significant TF effort against MM43112609 which is much larger than M(10^{10000000}) I do not know what program you would use to do this. 

20111102, 00:28  #4  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
24624_{8} Posts 
Quote:
M(11,111,111,111,111,111,111,111) has a factor of 5246666666666666666666614201 (which is 92 bits, I ran from 1 (72 actually) to 100 bits in less than 30 seconds on my laptop. I used Factor5. 

20111102, 00:38  #5 
"Daniel Jackson"
May 2011
14285714285714285714
719 Posts 
Sorry, that was supposed to say 2^{(10[sup]23}1)/9[/sup]1. Yes, 10^{100}+267 is the smallest prime greater than a googol. For factors of M(11111111111111111111111), they have to be of the form k*22222222222222222222222+1. For the latter, the prime factors have to be of the form k*2*(10^{100}+267)+1. I'll try Factor5. If it can't do M(10^{100}+267), which is about 10^{3.0103*10[sup]99}[/sup], then I'll need more help.
Last fiddled with by Stargate38 on 20111102 at 00:51 
20111102, 00:55  #6  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{2}×3×887 Posts 
Quote:
Quote:
Check the MersenneWiki: http://mersennewiki.org/index.php/Factor5 

20111102, 01:08  #7 
"Daniel Jackson"
May 2011
14285714285714285714
719 Posts 
Thanks. :)
M31415926535897932384626433832795028841 has no factors less than 2^{130} Last fiddled with by Stargate38 on 20111102 at 01:09 
20111102, 01:30  #8  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
24624_{8} Posts 
Quote:


20111102, 01:38  #9  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10100110010100_{2} Posts 
Quote:
Here is what you can put into your status.txt to continue it (assuming 2 threads. Code:
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000267 350 370 114674 3577768754 120245380239 0 0 2 0 

20111102, 13:12  #10 
"Daniel Jackson"
May 2011
14285714285714285714
719 Posts 
M909090909090909090909090909091 has a factor: 2548241818181818181818181818182073007
M111111111112111111111111 has a factor: 2000000000017999999999999 M7777777777772777777777777 has a factor: 1539999999999009999999999847 
20111102, 13:14  #11 
"Bob Silverman"
Nov 2003
North of Boston
2^{3}×3×311 Posts 

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