trial factoring with mfakto question
 

Newbie question here,what exactly is the purpose of trial factoring?Is it just to eliminate exponents or can you find primes(i don't mean it as simplistic as it sounds,i elaborate below):
I'm using my r9 290 with mfakto (which is good for trial factoring) and i see it tests factors within a certain range(expample 2^70 - 2^71) each time.So many people testing different ranges.If the last possible factors are tested by someone and it yields no results,then obviously it's a prime(correct me i'm wrong),sooo who gets the credit or...you know,how does it all work?

I'm not saying it's all about the credit or the glory( definetily not for money),but i'm just curious as to how it works.

Maybe i've got it all wrong and nothing above makes sense,do correct me.

Another question,can I chose a certain number to check at manual testing?I checked a number from 2^69 to 2^70 and I like this number,so can I chose to check it up to 2^80 or whatever?

[QUOTE=arbiter21;425203]Newbie question here,what exactly is the purpose of trial factoring?Is it just to exclude exponents or can you find primes(i don't mean it as simplistic as it sounds,i elaborate below):
I'm using my r9 290 with mfakto (which is good for trial factoring) and i see it tests factors within a certain range(expample 2^70 - 2^71) each time.So many people testing different ranges.If the last possible factors are tested by someone and it yields no results,then obviously it's a prime(correct me i'm wrong),sooo who gets the credit or...you know,how does it all work?

I'm not saying it's all about the credit or the glory( definetily not for money),but i'm just curious as to how it works.

Maybe i've got it all wrong and nothing above makes sense,do correct me.[/QUOTE]

I had a somewhat similar doubt when I started in 1997... :smile:
Tria-factoring scope is to check the Mersenne number for smaller divisors. If a divisor is foud, the number cannot be prime.
In your case, you are testing all the divisors in the range between 2[sup]70[/sup] and 2[sup]71[/sup].
As the exponent of the range rises, the range to be checked doubles (the range between 2[sup]71[/sup] and 2[sup]72[/sup] has twice the candidates of your actual range to be checked). It's easy to see that, doubling both the range and the size of the factors will lead to an increment of the time needed to complete it. There is a break-even line beyond which trial-factoring becomes more time-consuming than the primality testing (Lucas.Lehmer test).

The whole thing is a bit more complex, but it basically works as explained.

Luigi

[QUOTE=ET_;425205]I had a somewhat similar doubt when I started in 1997... :smile:
[/QUOTE]

I was born in 1997 :smile:
[QUOTE=ET_;425205]There is a break-even line beyond which trial-factoring becomes more time-consuming than the primality testing (Lucas.Lehmer test).
[/QUOTE]

But gpu's are good at trial factoring only,right?

[QUOTE=arbiter21;425206]
But gpu's are good at trial factoring only,right?[/QUOTE]

GPUs are REALLY good (up to 100x) at TF, and have the same efficience of a 12-core in Lucas-Lehmer and P-1 work.

[QUOTE=arbiter21;425206]I was born in 1997 :smile:


But gpu's are good at trial factoring only,right?[/QUOTE]

GPUs are good at trial factoring up to a certain level, after which point they are more efficient at LL testing (using clLucas)

The difference is that GPUs can go much higher in trial factoring than CPUs before you should switch over. A CPU might trial factor up to 68 before doing LL tests, a GPU could go to 72.

GPUs came on the scene later and there were a lot less of them in GIMPS than CPUs, which meant there was a ton of work in TF that was worth doing before those GPUs should be doing LL testing, at least from the perspective of the project as a whole. In the last year we have made big progress clearing out the gap of GPU TF work. Right now if you want to do double check work a reliable GPU is better off doing DC work than LL work since we have closed the gap.

For first time LL testing of a world record size prime, there is still enough TF work to be done in that range that GPUs should do that first, at least for the next several months. At some point we reach a break even where the GPUs forge ahead doing a little bit of TF then come back and help the CPUs with LL testing (or even P-1 testing first) until they need to forge ahead and clear out another set of candidates trial factored to the correct level.

Can mfakto do LL ,or generally anything else ,or just trial factoring?

[QUOTE=arbiter21;425210]Can mfakto do LL ,or generally anything else ,or just trial factoring?[/QUOTE]

mfakto can onnly do TF. There are other programs that can run LL on a GPU (I think clLucas is the right one for AMD GPUs, but as I use nVidia boards, I may be off)

Only a few graphic cards are good at LL: Geforce 590, 690, Titan, Titan Black, Titan Z (not Titan X), because it requires double precision performance.

Most of the popular cards for gaming: Titan X, 980, 980 Ti, 780, 780 Ti ... are very good at single precision performance which is good for trial factoring, but the double precision performance is only like 1/16th or 1/24th of SP. I would be a waste to do slow LL on those instead of doing fast trial factoring.

[url]http://www.mersenne.ca/cudalucas.php[/url]