2 TF (2^67) per day

[dsouza123]

What CPU and speed is/would be needed to do two Trial Factors per day (24 hours) ( complete 2^67 step and no further ) ?

64 bit CPU ? x86 ? Integer ? SSE2 at ? GHz ?

HT, hyperthreading OK, (dual core on same die is kind of cheating, really equivalent to a dual CPU box OR is it really just a very extreme way to get parallel (vector) processing like SSE2 ).

[smh]

It depends on the size of the exponent you are testing.

An exponent twice as large factors about twice as fast to the same bit level

[eepiccolo]

I assume you're talking about exponents currently being assigned by PrimeNet for TF, which are ~24M

The vast majority of the TFing time will be from 2^64 to 2^67 because the time doubles for each bit. So it's best to use a P4 because the P4 is much faster at 2^64 and higher because it has SSE2 instructions.

But now to address your original question about doing two TFs in one day without finding a factor on one CPU. I don't think a processor exists that could do that, because I actually have a P4 2.4 GHz doing TFs, and it takes 30 hours per exponent if it doesn't find a factor.

I don't know how fast a P4 3.2 GHZ would be TFing, but that processor would probably be the fastest. Perhaps someone with that processor would be willing to make a benchmark? My guess is it would take between 15 and 20 hours.

[dsouza123]

Yes, I was talking about TF at about 22M - 24M, the size that is currently being handed out, which the Prime95 displays for the highest factoring step
Factoring M23xxxxxx to 2^67
and when the 2^67 step is complete sends back the result.

From your data point of 30 hours for a 2.4 P4 it would seem that a 6 Ghz P4 would be required for a TF in 12 hours.
A 3 Ghz P4 would take 24 hours.

Unless this calculation is skewed by the slow processing to 2^63 inclusive, dropping the much faster SSE2 optimizated rate of 2^64 and above.
----
In response to smh How can factoring time be dependant on the size of the Mersenne number ? At a certain bit depth say 2^65 using the same PC shouldn't it be almost the same if a number would end up being factored to 2^67 or 2^69 ?

Is there a math or algorithmic reason or something else ?

[eepiccolo]

Originally posted by dsouza123
From your data point of 30 hours for a 2.4 P4 it would seem that a 6 Ghz P4 would be required for a TF in 12 hours.
A 3 Ghz P4 would take 24 hours.

The time won't be quite proportional like that, because faster P4s run at higher bus speeds, and can access the memory faster. That's why my estimate is less time than just extrapolating proportionally.

Originally posted by dsouza123
In response to smh How can factoring time be dependant on the size of the Mersenne number ? At a certain bit depth say 2^65 using the same PC shouldn't it be almost the same if a number would end up being factored to 2^67 or 2^69 ?

Is there a math or algorithmic reason or something else ?

Any factor of a Mersenne number 2^p - 1 has the form 2*k*p+1, where k is an integer, and p is the same exponent in both expressions. So you only have to test factors of the form 2*k*p+1. So as p increases, the number of possible factors up to a given limit (like 2^67) decreases, and in all practicality, the relationship is inversely proportional.

[PageFault]

Having done several 79M exponents to 72 bits it was my observation that this is more or less correct. Doing the 68 bit pass took about as long as the 66 bit pass on 19M using a reference 1333 tbird.

Nobody has factored until they get a 72 bit run done. It is agonizingly slow, on the reference tbird 70 to 72 bits took nearly four weeks. At least I did completely factor one of them, turned up a 69 bit trial factor - wonder if this is a GIMPS first?

Originally posted by dsouza123
At a certain bit depth say 2^65 using the same PC shouldn't it be almost the same if a number would end up being factored to 2^67 or 2^69 ?

[lycorn]

I tried TFing a couple of Mnumbers, with exps in the 28M range, from 64 to 67 bits, on a P4 B (533MHz FSB) 2.66 GHZ @ stock speed. The total time per exponent was slightly under 14 hours. I quickly got it back to LL testing ...

[markr]

Do we know who the patient soul was who TFd M79,299,959 to 2^74 ??? ...and found no factor.

I used to do more TF work when the exponents were still below 21.6M & the limit was 2^66.

[NookieN]

Originally posted by eepiccolo
I don't know how fast a P4 3.2 GHZ would be TFing, but that processor would probably be the fastest. Perhaps someone with that processor would be willing to make a benchmark? My guess is it would take between 15 and 20 hours.

I went ahead and tried it on a 3.3Ghz P4 with HT enabled. The TF of M235xxxx to 2^67 took 34 hours with another instance of Prime working on a LL test. I don't have any metrics on running two TFs right now, but I think the results would be fairly similar. So an HT-enabled 3.2Ghz box should be able to do 2 TFs in about 35 hours, while an HT-disabled box would take about 40-44 hours.

Hitting the 24-hour mark for 2 TFs would probably require about a 4.8-5Ghz HT-enabled chip.