P-1 factoring anyone?

[drh]

Thanks for your feedback. It does help to understand some of the nuances of this project. The math maybe above me, but I am learning, so thank you.

[Rodrigo]

Originally Posted by firejuggler

Don't worry, it is with 1 instance of mfaktc.
What i find straneg is that one core of my E8300 seem to be enough to 'feed' my GPU.
If I use 2 instance of Mfaktc, I should have about 85 to 90 Ghz/day

This is mind-blowing -- running 24/7, you could get over 32,000 GHz/days in one year from a single computer, for the price of a good graphics card.

In terms of both output and cost-effectiveness, it sounds so much superior to "ordinary" CPU crunching. I can't think of a better argument for putting one's GPU to work. So, why aren't more people doing this -- what's the catch?

Rodrigo

[James Heinrich]

Originally Posted by Rodrigo

So, why aren't more people doing this -- what's the catch?

• It's not built into Prime95 (... yet)
• Manual assignment getting and reporting
• Not everyone has a powerful graphics card
• Not everyone with a powerful graphics card has an NVIDIA card
• It interferes with working on the system more so than Prime95, especially on older (compute 1.x) cards

[Rodrigo]

Originally Posted by James Heinrich

• It's not built into Prime95 (... yet)
• Manual assignment getting and reporting
• Not everyone has a powerful graphics card
• Not everyone with a powerful graphics card has an NVIDIA card
• It interferes with working on the system more so than Prime95, especially on older (compute 1.x) cards

Ah, I see -- thanks!

I suppose one could buy the proper kind of card to put in a dedicated PC (not used for anything else). That would take care of the last three points. But in that case the second point would be a problem, as you'd have to keep going back to the "unattended" computer to get work and report results.

Much appreciated.

Rodrigo

[ET_]

Originally Posted by Rodrigo

Ah, I see -- thanks!

I suppose one could buy the proper kind of card to put in a dedicated PC (not used for anything else). That would take care of the last three points. But in that case the second point would be a problem, as you'd have to keep going back to the "unattended" computer to get work and report results.

Much appreciated.

Rodrigo

I usually reserve 1 or 2 weeks of work, and let the program run when I am at work, or during night, and stopping it when I need the PC. Even this way, I get a higher throughput than not using the program...

Luigi

[Commaster]

I've failed the 4th point, so I'm somewhat of "a bit disappointed" :(

[ixfd64]

I have a few questions about P-1 factoring:

1. I know that allocating more memory increases the chance of finding a factor (although the law of diminishing returns quickly kicks in after 1 GB or so). Does this just affect the chance of finding a factor, or does it also increase the size of a potential factor?

2. It's not unusual for large factors found by P-1 to be composite. In fact, most P-1 factors with 40 or more digits will split into two further factors. That having been said, has anyone ever found one that split into three factors?

3. Speaking of #2, are there any good ways of finding large prime P-1 factors?

[James Heinrich]

Originally Posted by ixfd64

1. I know that allocating more memory increases the chance of finding a factor (although the law of diminishing returns quickly kicks in after 1 GB or so). Does this just affect the chance of finding a factor, or does it also increase the size of a potential factor?

Increasing the memory allocation in and of itself simply makes the P-1 process more efficient, therefore faster. As a consequence, Prime95 will chose larger bounds if more memory is allocated, balancing the longer time it takes to process higher bounds vs the greater chance of finding factors. So yes, it does affect the chance of chance a factor.

You can play around with the balance of bounds, probability and RAM requirements on my P-1 probability calculator. Basic rule-of-thumb is that 10-30x the exponent is the suggested amount of RAM for a good P-1 (less than that will do a less-thorough P-1, more than that doesn't add much benefit). So if you're working on M50xxxxxx, then 500MB-1500MB is good.

Now I step back and let other, wiser people answer the rest of your quesitons.

[lorgix]

#2. Numbers exist such that any number of prime factors of a found factor is possible. I would bet a large sum of money that it has happened in Mersenne history.

#3. I don't think there is a way to do that. P-1 finds factors smooth to the specified bounds. The higher the bounds, the more likely it is that more than one factor is found. So strictly speaking... the lower the bounds, the more likely it is that the factor you find is prime rather than composite. But since lower bounds mean lower chance of finding a factor, that's just not a good idea. P-1 finds smooth factors, that's what it does. ECM can find factors that are practically impossible to find with P-1. And of course there are several other algorithms, all with their own strengths and weaknesses.


Disclaimer: By posting this I'm not implying that I'm any wiser than James.

[Brian-E]

Originally Posted by ixfd64

2. It's not unusual for large factors found by P-1 to be composite. In fact, most P-1 factors with 40 or more digits will split into two further factors. That having been said, has anyone ever found one that split into three factors?

Originally Posted by lorgix

#2. Numbers exist such that any number of prime factors of a found factor is possible. I would bet a large sum of money that it has happened in Mersenne history.

Presumably it would routinely happen that composite factors found by P-1 have 3 or more factors themselves if it were not for the fact that P-1 is generally only performed on Mersenne numbers that have already been unsuccessfully trial factored up to, say, 2^70. Smaller factors than that are therefore known not to exist, so only the rare huge P-1 finds of around 2^210 or greater can possibly turn up 3 factors of their own. If you did P-1 before any trial factoring it would be another story.

[ckdo]

It would be extremely nice if double-checked exponents >10M could actually be reserved for TF/P-1. I'm obviously not the only one "blindly" processing such at the risk of conflicting work effort currently.