P-1 factoring anyone? - Page 96

axn · 2012-01-05, 05:26

Quote:

Originally Posted by flashjh

Is there any way to P-1 very large exponents yet? I would like to P-1 a M999XXXXXX exponent.

Jerry

The largest implemented FFT size in P95 is 32MB whose limit is as mentioned. A 56M FFT should be able to test your exponent in question. It'd be relatively trivial for George to create it, but not sure if he's ina ny rush to do this

Without a suitable FFT implementation, there's no way to P-1 these exponent(s). How far have you TF-ed them?

flashjh · 2012-01-05, 06:15

Quote:

Originally Posted by axn

The largest implemented FFT size in P95 is 32MB whose limit is as mentioned. A 56M FFT should be able to test your exponent in question. It'd be relatively trivial for George to create it, but not sure if he's ina ny rush to do this

Without a suitable FFT implementation, there's no way to P-1 these exponent(s). How far have you TF-ed them?

Thanks for the info. The exponent was TFd to 79, not by me. I was looking at some reports and saw a few M999XXXXXX exponents that needed P-1. So I grabbed one to test on my P-1 system only to find that it doesn't work. That's when I went reading and found the current limit for P-1. I searched for an update but didn't find it (until now). Hopefully when v27.1 x64 is final it will allow the bigger FFTs?

axn · 2012-01-05, 06:26

Quote:

Originally Posted by flashjh

Thanks for the info. The exponent was TFd to 79, not by me.

I think the optimal TF depth is around 81-82 bits by CPU or 84-85 bits by GPU. If you have access to a GPU, I suggest to TF it all the way to 84 bits _at least_, before even contemplating about P-1.

LaurV · 2012-01-05, 07:31

Seconding axn. In fact, raising: There are only 13 expos TF-ed to 79, and all are 999'96x'xxx or higher. Thinking how long a LL would take for one of that, and thinking we would TF at least 1% of the time worth of it, then there would make no sense to think about P-1, and to ever dream about LL unless they are TF-ed to at least 82-83 bits on CPU, or 86-87 bits on GPU.

flashjh · 2012-01-05, 08:06

Quote:

Originally Posted by LaurV

Seconding axn. In fact, raising: There are only 13 expos TF-ed to 79, and all are 999'96x'xxx or higher. Thinking how long a LL would take for one of that, and thinking we would TF at least 1% of the time worth of it, then there would make no sense to think about P-1, and to ever dream about LL unless they are TF-ed to at least 82-83 bits on CPU, or 86-87 bits on GPU.

TF to 87 bits estimated completion via one core on my CPU is 2036-09-12 00:36, not going to happen

. Still waiting on an ETA from mfaktc...

LaurV · 2012-01-05, 19:15

Quote:

Originally Posted by flashjh

Still waiting on an ETA from mfaktc...

Didn't want to say before doing it, so I just did a 77 to 78 of 999'998'687 which took a bit less then 5 hours using about 45% of one of my GPU's (and got 30 GHz-days for it!). That would be about 95 days to go for 86 to 87 bits, or about 190 days to go all the way from 0 to 87. Well, maybe we could start P-1 a bit earlier

. But anyhow, that is dreaming, and LL is sleeping dead, for these exponents.

S34960zz · 2012-01-05, 20:10

http://mersenne-aries.sili.net/expon...ails=999999131

245 GHz-days to TF to 80
730 GHz-days for default P-1 for M999999131
27583 days to LL once.

"You're gonna need a [faster CPU]" --Police Chief Martin Brody

James Heinrich · 2012-01-05, 20:15

Quote:

Originally Posted by LaurV

Didn't want to say before doing it, so I just did a 77 to 78 of 999'998'687 which took a bit less then 5 hours using about 45% of one of my GPU's (and got 30 GHz-days for it!). That would be about 95 days to go for 86 to 87 bits, or about 190 days to go all the way from 0 to 87. Well, maybe we could start P-1 a bit earlier

. But anyhow, that is dreaming, and LL is sleeping dead, for these exponents.

2⁸⁶-2⁸⁷ would take 15,671 GHz-days
2⁷⁸-2⁸⁷ would take 31,282 GHz-days (starting from where it is now)
2¹-2⁸⁷ would take 31,342 GHz-days (starting from scratch)
You can get an approximate idea of how many GHz-days/day your GPU can process here.

flashjh · 2012-01-05, 20:31

Quote:

Originally Posted by LaurV

Didn't want to say before doing it, so I just did a 77 to 78 of 999'998'687 which took a bit less then 5 hours using about 45% of one of my GPU's (and got 30 GHz-days for it!). That would be about 95 days to go for 86 to 87 bits, or about 190 days to go all the way from 0 to 87. Well, maybe we could start P-1 a bit earlier

. But anyhow, that is dreaming, and LL is sleeping dead, for these exponents.

Has anyone used Moore's law to project when CPUs / GPUs will feasibly be able to LL these exponents?

James Heinrich · 2012-01-05, 20:41

Quote:

Originally Posted by flashjh

Has anyone used Moore's law to project when CPUs / GPUs will feasibly be able to LL these exponents?

Depends how you define "feasible", but I'd say roughly 15 years to be able to LL M999M on common hardware in approximately 1 month.

chalsall · 2012-01-05, 20:56

Quote:

Originally Posted by James Heinrich

Depends how you define "feasible", but I'd say roughly 15 years to be able to LL M999M on common hardware in approximately 1 month.

My god!!! I hadn't thought about it, but you're probably correct!

By that time our systems will be so powerful that Perl (and PHP et al languages) will have modules which can be included to implement the "DWIM" directive....

(DWIM: Do What I Mean (not what I told you to do).)

2012-01-05, 20:10	#1052
S34960zz Feb 2011 2²·13 Posts	Jaws exponents http://mersenne-aries.sili.net/expon...ails=999999131 245 GHz-days to TF to 80 730 GHz-days for default P-1 for M999999131 27583 days to LL once. "You're gonna need a [faster CPU]" --Police Chief Martin Brody

2012-01-05, 07:31	#1049
LaurV Romulan Interpreter Jun 2011 Thailand 2·3·1,609 Posts	Seconding axn. In fact, raising: There are only 13 expos TF-ed to 79, and all are 999'96x'xxx or higher. Thinking how long a LL would take for one of that, and thinking we would TF at least 1% of the time worth of it, then there would make no sense to think about P-1, and to ever dream about LL unless they are TF-ed to at least 82-83 bits on CPU, or 86-87 bits on GPU.