Program to TF Mersenne numbers with more than 1 sextillion digits?

Stargate38 · 2011-11-01, 19:31

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)?

Christenson · 2011-11-01, 22:52

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!!!!

Mr. P-1 · 2011-11-01, 23:10

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(10^10000000)

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

Uncwilly · 2011-11-02, 00:28

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.

Stargate38 · 2011-11-02, 00:38

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 10^{3.0103*10[sup]99}[/sup], then I'll need more help.

Uncwilly · 2011-11-02, 00:55

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 10^{3.0103*10[sup]99}[/sup], then I'll need more help.

It can, no factors between 330 bits and 350 bits. (2 minutes)

Quote:

Originally Posted by Stargate38

Where can I download Factor5? I can't find it on Google.

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

Stargate38 · 2011-11-02, 01:08

Thanks. :)

M31415926535897932384626433832795028841 has no factors less than 2¹³⁰

Uncwilly · 2011-11-02, 01:30

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.

Uncwilly · 2011-11-02, 01:38

Quote:

Originally Posted by Stargate38

I'll try Factor5. If it can't do M(10¹⁰⁰+267), which is about 10^{3.0103*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

Stargate38 · 2011-11-02, 13:12

M909090909090909090909090909091 has a factor: 2548241818181818181818181818182073007
M111111111112111111111111 has a factor: 2000000000017999999999999
M7777777777772777777777777 has a factor: 1539999999999009999999999847

R.D. Silverman · 2011-11-02, 13:14

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?

2011-11-01, 19:31	#1
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2C4₁₆ 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)?

2011-11-02, 00:38	#5
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2²×3×59 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 k22222222222222222222222+1. For the latter, the prime factors have to be of the form k2(10¹⁰⁰+267)+1. I'll try Factor5. If it can't do M(10¹⁰⁰+267), which is about 10^{3.010310[sup]99}[/sup], then I'll need more help. Last fiddled with by Stargate38 on 2011-11-02 at 00:51

2011-11-02, 01:08	#7
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2²·3·59 Posts	Thanks. :) M31415926535897932384626433832795028841 has no factors less than 2¹³⁰ Last fiddled with by Stargate38 on 2011-11-02 at 01:09

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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!!!!

2011-11-02, 13:12	#10
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2²·3·59 Posts	M909090909090909090909090909091 has a factor: 2548241818181818181818181818182073007 M111111111112111111111111 has a factor: 2000000000017999999999999 M7777777777772777777777777 has a factor: 1539999999999009999999999847