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 2011-11-01, 19:31 #1 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 673 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(10100+267)?
 2011-11-01, 22:52 #2 Christenson     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 (2^23-1)/9 factors of 2.....unless you forgot to subtract a one somewhere!!!!
2011-11-01, 23:10   #3
Mr. P-1

Jun 2003

7×167 Posts

Quote:
 Originally Posted by Stargate38 What program can do a Trial factor on 2(10[sup]23-1)/9[/sup]? Is it out of Prime95's range?
I believe so.

Quote:
 Is there a way to TF M(10100+267)?
That's perfectly feasible. To test a single candidate factor 2kp+1 of the Mersenne number Mp, you need to do roughly log2(p) squarings mod (2kp+1). If p=10100+267, then the number of squarings modulo a one-hundred-and-something digit number is approximately 100log2(10) = 267. A typical desktop could do thousands of tests per second with a negligable memory footprint.

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(1010000000)

I do not know what program you would use to do this.

2011-11-02, 00:28   #4
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

10,007 Posts

Quote:
 Originally Posted by Stargate38 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(10100+267)?
I take it that you meant $2^{(10^{23}-1)/9} -1$, the exponent being: 11,111,111,111,111,111,111,111.

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.

 2011-11-02, 00:38 #5 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 673 Posts Sorry, that was supposed to say 2(10[sup]23-1)/9[/sup]-1. Yes, 10100+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*(10100+267)+1. I'll try Factor5. If it can't do M(10100+267), which is about 103.0103*10[sup]99[/sup], then I'll need more help. Last fiddled with by Stargate38 on 2011-11-02 at 00:51
2011-11-02, 00:55   #6
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

1000710 Posts

Quote:
 Originally Posted by Stargate38 For factors of M(11111111111111111111111), they have to be of the form k*22222222222222222222222+1.
The one that I reported is.

Quote:
 Originally Posted by Stargate38 I'll try Factor5. If it can't do M(10100+267), which is about 103.0103*10[sup]99[/sup], then I'll need more help.
It can, no factors between 330 bits and 350 bits. (2 minutes)

Quote:
Check the MersenneWiki: http://mersennewiki.org/index.php/Factor5

 2011-11-02, 01:08 #7 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 67310 Posts Thanks. :) M31415926535897932384626433832795028841 has no factors less than 2130 Last fiddled with by Stargate38 on 2011-11-02 at 01:09
2011-11-02, 01:30   #8
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

10,007 Posts

Quote:
 Originally Posted by Stargate38 Thanks. :) M31415926535897932384626433832795028841 has no factors less than 2130
You can use the tool on James H's site: http://mersenne-aries.sili.net/ to check how many bits to start at. You can find the tool at the bottom of the box on the right. See the attachment.
Attached Thumbnails

2011-11-02, 01:38   #9
Uncwilly
6809 > 6502

"""""""""""""""""""
Aug 2003
101×103 Posts

10,007 Posts

Quote:
 Originally Posted by Stargate38 I'll try Factor5. If it can't do M(10100+267), which is about 103.0103*10[sup]99[/sup], then I'll need more help.
Quote:
 Originally Posted by Uncwilly It can, no factors between 330 bits and 350 bits. (2 minutes)
I started 350 to 370 and halted at 0.404% done. No factors.
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

 2011-11-02, 13:12 #10 Stargate38     "Daniel Jackson" May 2011 14285714285714285714 673 Posts M909090909090909090909090909091 has a factor: 2548241818181818181818181818182073007 M111111111112111111111111 has a factor: 2000000000017999999999999 M7777777777772777777777777 has a factor: 1539999999999009999999999847
2011-11-02, 13:14   #11
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by Stargate38 M909090909090909090909090909091 has a factor: 2548241818181818181818181818182073007 M111111111112111111111111 has a factor: 2000000000017999999999999 M7777777777772777777777777 has a factor: 1539999999999009999999999847
Is there some point to all of this?

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