24 hour rally

[mdettweiler]

Originally Posted by em99010pepe

I think the AMD's are poor on overclocking, at least that was what I've been reading on different forums.

Just received an interesting private message from Beyond, you guys should take a look on the stats next Wed or Thursday. lol

I didn't think of overclocking at all, actually.

As for the message from Beyond: let me guess, he got more quadcores?

[gd_barnes]

Originally Posted by Anonymous

As for pulling out the heavy artillery--Gary, you need a quad-core! (Hey, the new AMD Phenoms--which are true quad-cores, unlike the Core 2 Quads--are getting pretty cheap now, and that's driven down the price of the Intel quads, too. You might want to check it out.)

I have to admit I'm getting a little too caught up in this but I can't let myself do it. I could get in some serious trouble if I try to bring too much to the rally. Expect me to bring about 9-10 cores; 2-3 more than last time at full strength and 4-5 more than when my son's laptop was shut down for the evening.

You're right, I need a quad-core and will probably get one later this year.

Carlos, I welcome all of the firepower that you're bringing to the project. Bring the whole world and we'll hit n=600K on all k's in March! I/we will accomodate as many people as you can bring.

I have a better idea on this weekend's rally that could give Free-DC a good goal to shoot for: See if you can best all other teams including the 'none' team COMBINED!! Or in other words, see if you can do over 50% of all of the testing. With what you're bringing, I think that would make things very interesting. I've always said that no matter how big or how good you are at something, you can always challenge yourself in ways to make yourself bigger or better.

Here's the deal I'd like to offer Free-DC and all of the large computing-power teams: I have some huge goals for not just this range of k, but for prime searching in general; Proth primes, Riesel primes, twin primes, Generalized Fermat's, Riesel/Sierpinski conjectures, you name it. If you leave some of your computing power here, I can guarantee you that there will be many interesting rallies and searches in the future with fully sieved files ready for testing.

My biggest goal is to find 'biases' in the distribution of primes and that can only be done with extremely accurate and contiguous lists of them. By that I mean biases in specific prime forms, k-values, n-values, or whatever that yield a higher percentage of primes than the average after sieving to a specific depth. (Note that this is different than simple high-weight k's that yield no higher percentage of primes from remaining candidates after sieving to a specific depth than do average-weight k's.)

One example that we already have for a positive bias: Generalized Fermat #'s, i.e. primes of the form P=b^n+1. It is proven that P can only be prime if n is a power of 2 so we can quickly 'sieve' out all other n-values. For the remaining n=2^q, P can only have prime factors of the form 2k*2^q+1. In 'plain English', that means if the form has an exponent of n=8192, the factors must be a multiple of 8192*2=16384 greater than 1, i.e. 16385, 32769, 49153, 65537, etc. and since 65537 is the first prime # in that sequence, it is the smallest possible factor for any base for b^8192+1. But the key is the few possibilities for factors even after sieving to high factor-ranges.

Finding a good bias also requires good software that searches the form that you're interested in nearly as fast as LLR can search k*2^n-1. Proth almost accomplishes this with GFn's, only timing about 10-20% longer for similar-sized primes but it is more than made up for the higher percentage of primes found as a result of the small possibilities for factors. The top-5000 site reflects this bias with many of the top 50 largest non-Mersenne primes being GFn's.

I believe other such biases like this exist. The key is extensive analysis of contiguously searched and double-checked ranges of primes. That is why I started this project with assistance from Karsten Bonath! It's all about getting the ranges searched and checked and then the analysis can begin!


Gary

[mdettweiler]

Originally Posted by gd_barnes

I have to admit I'm getting a little too caught up in this but I can't let myself do it. I could get in some serious trouble if I try to bring too much to the rally. Expect me to bring about 9-10 cores; 2-3 more than last time at full strength and 4-5 more than when my son's laptop was shut down for the evening.

You're right, I need a quad-core and will probably get one later this year.

Carlos, I welcome all of the firepower that you're bringing to the project. Bring the whole world and we'll hit n=600K on all k's in March! I/we will accomodate as many people as you can bring.

I have a better idea on this weekend's rally that could give Free-DC a good goal to shoot for: See if you can best all other teams including the 'none' team COMBINED!! Or in other words, see if you can do over 50% of all of the testing. With what you're bringing, I think that would make things very interesting. I've always said that no matter how big or how good you are at something, you can always challenge yourself in ways to make yourself bigger or better.

Now that is an interesting idea! It will be interesting to see if Free-DC can do it.

Originally Posted by gd_barnes

Here's the deal I'd like to offer Free-DC and all of the large computing-power teams: I have some huge goals for not just this range of k, but for prime searching in general; Proth primes, Riesel primes, twin primes, Generalized Fermat's, Riesel/Sierpinski conjectures, you name it. If you leave some of your computing power here, I can guarantee you that there will be many interesting rallies and searches in the future with fully sieved files ready for testing.

My biggest goal is to find 'biases' in the distribution of primes and that can only be done with extremely accurate and contiguous lists of them. By that I mean biases in specific prime forms, k-values, n-values, or whatever that yield a higher percentage of primes than the average after sieving to a specific depth. (Note that this is different than simple high-weight k's that yield no higher percentage of primes from remaining candidates after sieving to a specific depth than do average-weight k's.)

One example that we already have for a positive bias: Generalized Fermat #'s, i.e. primes of the form P=b^n+1. It is proven that P can only be prime if n is a power of 2 so we can quickly 'sieve' out all other n-values. For the remaining n=2^q, P can only have prime factors of the form 2k*2^q+1. In 'plain English', that means if the form has an exponent of n=8192, the factors must be a multiple of 8192*2=16384 greater than 1, i.e. 16385, 32769, 49153, 65537, etc. and since 65537 is the first prime # in that sequence, it is the smallest possible factor for any base for b^8192+1. But the key is the few possibilities for factors even after sieving to high factor-ranges.

Finding a good bias also requires good software that searches the form that you're interested in nearly as fast as LLR can search k*2^n-1. Proth almost accomplishes this with GFn's, only timing about 10-20% longer for similar-sized primes but it is more than made up for the higher percentage of primes found as a result of the small possibilities for factors. The top-5000 site reflects this bias with many of the top 50 largest non-Mersenne primes being GFn's.

I believe other such biases like this exist. The key is extensive analysis of contiguously searched and double-checked ranges of primes. That is why I started this project with assistance from Karsten Bonath! It's all about getting the ranges searched and checked and then the analysis can begin!


Gary

Hmm...quite interesting. Well, if you think about it, that is, essentially, the reason why prime searching is useful: to eventually find a pattern/formula for primes. If you're not going for an ultimate pattern/formula, then it's just a time sink.

The Generalized Fermat numbers you were talking about sound quite interesting. Is there a central status/reservation site for them by any chance?

[mdettweiler]

Originally Posted by Anonymous

Now that is an interesting idea! It will be interesting to see if Free-DC can do it.

I was just looking at the LLRnet stats, and I realized something: Free-DC is already doing more than 50% of all LLRnet testing! (According to the stats table, they currently account for 67.944% of all LLRnet testing). Whoops.

Okay, I guess that means we should set a higher goal for Free-DC: Maybe 75% of all LLRnet testing?

[gd_barnes]

Originally Posted by Anonymous

I was just looking at the LLRnet stats, and I realized something: Free-DC is already doing more than 50% of all LLRnet testing! (According to the stats table, they currently account for 67.944% of all LLRnet testing). Whoops.

Okay, I guess that means we should set a higher goal for Free-DC: Maybe 75% of all LLRnet testing?

Nah. I think there's a few people like me who will add several cores just for the rally. I'm only running 3 cores on the NPLB LLRnet upper range right now (will go to 9-10 for the rally). I'm thinking people from other teams adding cores will make it interesting for Free-DC to get 50%.

I can't spare my home sieving machines for more than a day because 300<k<400 is the #1 priority at the moment. If I could, I'd also be helping you with the double-check sieving.

I will have a few resources free up after n=260K-600K is done sieving to P=6T and major resources free up in mid-late March when n=600K-1M is done. After breaking off n=260K-600K, I'm thinking P=11T-12T will be optimal for the remainder.


Gary

[gd_barnes]

Originally Posted by Anonymous

Now that is an interesting idea! It will be interesting to see if Free-DC can do it.


Hmm...quite interesting. Well, if you think about it, that is, essentially, the reason why prime searching is useful: to eventually find a pattern/formula for primes. If you're not going for an ultimate pattern/formula, then it's just a time sink.

The Generalized Fermat numbers you were talking about sound quite interesting. Is there a central status/reservation site for them by any chance?

It's mostly a time sink anyway. What I enjoy is the math. Even though I like the ease of co-managing a project such as this one, I enjoyed setting up the web pages on the CRUS project a lot more. Also, the strange people that actually like this kind of 'wierd stuff' too and that you get to chat with also make it kind of fun.

On the GFn's, check out the top-5000 site projects. There's 2-3 of them related to Generalized fermat numbers and Generalized fermat FACTORS. It's the former that has the 'bias' that I'm talking about.

The GFn projects, for the most part, are not for the faint of heart. Due to the inherent 'positive bias', most have been searched very high. Unless you're willing to go in with some serious firepower, I'd not suggest using your resources. I'd somewhat compare it to LLRing for Riesel Sieve or 3*2^n-1; perhaps not quite that bad. Check them out. There might be some smaller top-5000 primes to go after.

The math on those can get a little complicated and I don't understand some of the symbols that they use but I'm sure once you get familiar with it, it wouldn't be too bad. Regardless, if you're only searching for primes, you don't have to understand the math...just how to load and use the software!

Edit: I was smoking something on the factor formula for GFn's in my prior post. It is now corrected in my post and Anon's response. Hopefully I got it corrected before anybody noticed. lol


Gary

[Flatlander]

For the rally I think you should redirect anything that's not from Free-DC to the port 300 server. Let them polish off all the low stuff while we find all the top 5000 primes!

[IronBits]

You are too kind. ;)

IF you created official stats at least daily, more folks would come.
If you created stats hourly, even more folks would come. :)

[mdettweiler]

Originally Posted by gd_barnes

Nah. I think there's a few people like me who will add several cores just for the rally. I'm only running 3 cores on the NPLB LLRnet upper range right now (will go to 9-10 for the rally). I'm thinking people from other teams adding cores will make it interesting for Free-DC to get 50%.

I can't spare my home sieving machines for more than a day because 300<k<400 is the #1 priority at the moment. If I could, I'd also be helping you with the double-check sieving.

I will have a few resources free up after n=260K-600K is done sieving to P=6T and major resources free up in mid-late March when n=600K-1M is done. After breaking off n=260K-600K, I'm thinking P=11T-12T will be optimal for the remainder.


Gary

Oh, I see. I thought you were talking about 50% overall, not just the rally.

[mdettweiler]

Originally Posted by gd_barnes

It's mostly a time sink anyway. What I enjoy is the math. Even though I like the ease of co-managing a project such as this one, I enjoyed setting up the web pages on the CRUS project a lot more. Also, the strange people that actually like this kind of 'wierd stuff' too and that you get to chat with also make it kind of fun.

On the GFn's, check out the top-5000 site projects. There's 2-3 of them related to Generalized fermat numbers and Generalized fermat FACTORS. It's the former that has the 'bias' that I'm talking about.

The GFn projects, for the most part, are not for the faint of heart. Due to the inherent 'positive bias', most have been searched very high. Unless you're willing to go in with some serious firepower, I'd not suggest using your resources. I'd somewhat compare it to LLRing for Riesel Sieve or 3*2^n-1; perhaps not quite that bad. Check them out. There might be some smaller top-5000 primes to go after.

The math on those can get a little complicated and I don't understand some of the symbols that they use but I'm sure once you get familiar with it, it wouldn't be too bad. Regardless, if you're only searching for primes, you don't have to understand the math...just how to load and use the software!

Edit: I was smoking something on the factor formula for GFn's in my prior post. It is now corrected in my post and Anon's response. Hopefully I got it corrected before anybody noticed. lol


Gary

Okay, thanks for the info. I'll check it out!

[mdettweiler]

Originally Posted by IronBits

You are too kind. ;)

IF you created official stats at least daily, more folks would come.
If you created stats hourly, even more folks would come. :)

The stats already are updated daily most of the time. Unfortunately, though, to do them hourly, we'd need a major overhaul of the LLRnet server system--it would need to be run on the same system that hosts the stats site (it's currently not), and work with MySQL and all that stuff so it could do automatic updates.