Holy new Mersenne prime, Batman! (M47 related)

[ixfd64]

Originally Posted by ewmayer

Your math seems suspect - in algebraic terms your are saying that solving the 2 uncoupled linear algebraic equations

55 + 6.3*x = 100

and

22 + 7.0*y = 100

yields y < x.

"Does not compute"...

It appears that Tony started on September 2 instead of September 1. In this case, he's doing about 11% each day.

Oh, and today is exactly two years to the day that M44 was discovered. It seems the verification will be done on September 11, the day M44 was verified!

[T.Rex]

Originally Posted by ewmayer

Due to some multithreaded performance issues which will be the subject of ongoing analysis, Rob Giltrap and Tom Duell of Sun are doing their Mlucas-based verify run using an FFT length of 4096K, which is much larger than really needed based on roundoff error considerations. Thankfully, some blazingly fast hardware [and excellent multithreaded performance at least at that FFT length] is helping to mitigate the resulting performance hit.
By the time the next M-prime discovery rolls around, my intention is to have the thread-related issues worked out and be able to do the verify in a week or less. At least that's the plan.

I'll see tomorrow which FFT length is used now by Glucas. I remember I've seen several messages at the beginning saying that Glucas has increased the FFT length in order to reduce the level of error under the required limit. So, maybe it is a general effect of this exponent to any FFT code, maybe because the exponent is close to some limit...
I'm using a 16x Itanium2 1.6 Ghz NUMA machine. And I've used some specific code and some special features of the Bull Linux version in order to have such a terrific speed. Can you remind us which machine you are using (type, frequency, number of CPUs), and the OS ?
Here is the SPEC CFP2006 result of the processor of my machine : SPEC.
I cannot imagine you can verify this prime in only 1 week or less, improving from about 14 days to 7, by simply improving the multi-threading. Once I'm able to compile Mlucas on the machine (execution error for now), we'll see.
However, I guess that the biggest version of the future Bull super-computer will enable to test this prime in only... 1 day. In 2009 or 2010... (All technical details are still confidential, for sure. Wait for official announcements next year.)
Tony

[T.Rex]

Originally Posted by ixfd64

Oh, and today is exactly two years to the day that M44 was discovered. It seems the verification will be done on September 11, the day M44 was verified!

Humm, not exact. The Press release of the announcement was ready the 09/11, meaning that 2 verifications were done before. So, probably that these 2 verifications were done the 10th. And the second verification of this prime will be done at least the 13th. So, it is not exactly the same dates (10-11 and 13-14), but it is VERY close !
Tony

[T.Rex]

Originally Posted by ixfd64

It appears that Tony started on September 2 instead of September 1.

I've started Monday 1rst at about 9am USA East Coast, but it took 1 day before I fixed some problems and reached the maximum speed.
Tony

[ewmayer]

Originally Posted by T.Rex

I'll see tomorrow which FFT length is used now by Glucas. I remember I've seen several messages at the beginning saying that Glucas has increased the FFT length in order to reduce the level of error under the required limit. So, maybe it is a general effect of this exponent to any FFT code, maybe because the exponent is close to some limit...
I'm using a 16x Itanium2 1.6 Ghz NUMA machine. And I've used some specific code and some special features of the Bull Linux version in order to have such a terrific speed. Can you remind us which machine you are using (type, frequency, number of CPUs), and the OS ?

I don't want to comment on the precise FFT length - and would urge the other verifiers to also refrain from doing so - because that might be too big a tipoff as to the exponent size. But I strongly suspect both Prime95 and Glucas are using the same FFT length, because it should be ample for testing the number in question.

I'll let Rob Giltrap answer the "hardware details" question, if he feels like doing so prior to the completion of the verify and the [hoped-for] official announcement.

[mdettweiler]

All this discussion regarding the verifications has gotten me wondering: what are the main differences between Glucas and Mlucas? I know they're both multi-threaded LL testing apps written in generic programming languages so they're non-architecture-specific, but not much more than that.

[ATH]

Originally Posted by ewmayer

By the time the next M-prime discovery rolls around, my intention is to have the thread-related issues worked out and be able to do the verify in a week or less. At least that's the plan.

So assuming M46 is 45M-50M, and it could be much bigger, completing it in a week would be 12.1-13.4 ms/iteration. For comparison my Core2Quad Q9450 2.66Ghz is doing 26.9ms on a 46M exponent with all 4 cores working on it.

Btw when all 4 cores are working on one LL, the cpu usage is alternating between 89% and 95%.

However, I guess that the biggest version of the future Bull super-computer will enable to test this prime in only... 1 day. In 2009 or 2010... (All technical details are still confidential, for sure. Wait for official announcements next year.)

DROOL (but can it play Crysis?!?!?!?)
(Actually I never ever played Crysis, I just think its funny it has become "standard" remark the last 6-12months to all news about impressive hardware).

Originally Posted by Jeff Gilchrist

Cool, I learned something new. I thought Prime95's multi-threaded feature allowed you to automatically run 4 LL tests or factoring simultaneously (if you had 4 CPUs), I didn't realize it let you do a multi-threaded LL test to speed up individual tests.

I never got it use more than one core on a single ECM curve, is it possible? I'm just curious, as you can easily to 1 curve on each core. I *think* I used all 4 cores on the last P-1 test, but not sure.

[ixfd64]

George usually gives hints each time a Mersenne prime is reported. However, he didn't give us anything this time, other than an estimate on the completion date of the verification.

I think there are two reasons for this:

1. The new prime is smaller than 10 million digits, and George doesn't want us to be disappointed from the very start.
2. The new prime is larger than 10 million digits, and George wants it to be a surprise.

I'm betting it's the latter case.

[T.Rex]

Originally Posted by Anonymous

All this discussion regarding the verifications has gotten me wondering: what are the main differences between Glucas and Mlucas? I know they're both multi-threaded LL testing apps written in generic programming languages so they're non-architecture-specific, but not much more than that.

Glucas stands for G(uillermo Ballester Valor)lucas. See: Glucas for more informations. Guillermo did 99.99 % of the work, I think. I only helped a few about the multi-threading. Maybe Guillermo or Ernst could provide some comparison about the different approaches, more than the multithreading is done by the 2 different verify codes [Glucas and Mlucas] is very different [fine-grain vs coarse-grain]..
T.

[mdettweiler]

Originally Posted by T.Rex

Glucas stands for G(uillermo Ballester Valor)lucas. See: Glucas for more informations. Guillermo did 99.99 % of the work, I think. I only helped a few about the multi-threading. Maybe Guillermo or Ernst could provide some comparison about the different approaches, more than the multithreading is done by the 2 different verify codes [Glucas and Mlucas] is very different [fine-grain vs coarse-grain]..
T.

Ah, I see. So, based on what I read on the website, I take it that the primary difference is that Mlucas is written in Fortran, whereas Glucas is written in C? (i.e., the main advantage of one over the other is whichever type of compiler you have that will produce the fastest and most efficient binary?)

[ewmayer]

Originally Posted by Anonymous

Ah, I see. So, based on what I read on the website, I take it that the primary difference is that Mlucas is written in Fortran, whereas Glucas is written in C?

Whatever website you got the "Fortran" bit from is 10 years out of date.