Davieddy's World

[Prime95]

Upon further reflection, a rough estimate for calculating number of LL tests saved:

P = prob. of P-1 finding a factor = .04
E = LL error rate = .02
C = cost of a P-1 run = .03 * LL cost

A TF factor saves:

C + (1 - P) * (2 + 2 * E) = .03 + .96 * 2.04 = 1.99 LL tests

A DCTF factor saves:

(1 + 2 * E) = 1.04 LL tests

So, ignore my previous post - James' estimated optimal TF levels are pretty darn close. Refining my estimates for P, E, and C shouldn't change the fact that James' chart is within about 1% of optimal.

[davieddy]

Originally Posted by swl551

Daviddy, you have the skills and the tenacity of a very successful car salesman. However, here, your style isn't making the sell. Do you really expect to win the minds any longer? I would've thrown in the towel by now and basically ditched these "fools". I think you enjoy the fight too much for your own entertainment. Thanks for keeping me entertained though.

Too late to stop now

D

[davieddy]

Originally Posted by davieddy

Another example which seems to be going over people's heads ATM, is that a 10% advance in the wavefronts per year results in one new prime per 4 years on average

Originally Posted by Prime95

This is irrelevant to GIMPS. We don't have a schedule, we find primes at whatever rate our compute power and luck allow.

I hope I can provoke you into second thoughts on this one.

By "luck" I presume you are referring to the "Poisson" nature of our quest, (although five more Curtis Coopers turning up on the doorstep would not go amiss).
The Poisson distribution is characterized by a single parameter (e.g. lifetime or half-life etc). I would say that our (interminable) deliberations on optimal TF levels (much as some of us enjoy doing it for its own sake) had the ultimate common goal of minimizing the expected time to the next prime which corresponds directly with the advance of the LL wavefronts.

Now the rate of completion of LLs is coming on very nicely (THX primarily to AVX and GPUs). However, I am not so confident that the allocation of LLs is going to allow this progress to be sustained.
GIGO, and I think you will agree that the allocation is on the garbagy side ATM.
IMO, this is partly down to the effect of interference from TF.
I feel strongly that TF to the feasible level should be completed further ahead of the LL allocation than it is at present. This would also give P-1 more of a chance of being done at something like the desirable rate.

Although Chalsall and I will fight each other over anything, I think this is the root cause of our current disagreement.

David

[davieddy]

Originally Posted by davieddy

Note how clearly James' graphs follow my simple rule that the bitlevel should increment when the exponent increases by 1.26 (time on TF remains proportional to time for an LL test).

Originally Posted by Aramis Wyler

James' graph is a curve. The bottom end maps to 1.25, the top end maps to 1.3. Yes, there is a point on the curve where the 1 bitlevel increment maps to 1.26. We can call that the troll point on the graph. Good try.

Originally Posted by axn

1.26 is a rule-of-thumb. And it is a pretty good ROT. There is a sound mathematical basis for that ROT. I'll take your word that the actual ratio is in the 1.25-1.3 range -- I'd consider that as excellent conformance to the ROT value.

Originally Posted by Aramis Wyler

Maybe it is a reasonable rule of thumb, but we're not exactly working the numbers out in our heads as we walk down the streets. Why would we dogmatically set a line using a rule of thumb for a site that is doing terraflops of calculations? We have the processing power to work out an actual rule.

Originally Posted by davieddy

Speak for yourself. That is exactly the sort of thing I do, giving me an overall view of the situation that won't be too far from a narrower, short term, unjustifiably precise approach, and easy to grasp.

The ROT arises as follows:
1) the time to TF from 73 to 74 is proportional to 1/expo
2) the time to TF from 73 to 74 is double that for 72 to 73 for a given expo.
3) The time for an LL test is proportional to expo².

If the exponent increases by 2^1/3 (=1.26) the times for TF and LL are both increased by 2^2/3.

Originally Posted by Prime95

Very close:

FFT = n log n
LL = n FFTs = n² log n

An example of a very important rule of thumb is that the hydrogen spectrum is closely modelled by differences in 1/n².
Although there are fine details, these are best considered as small differences from the ROT.

Apart from the log n which George mentions, there is also the probability of finding a factor being 1/73 or 1/74.
Excercise for you: how do these refinements influence the ROT?

Of course hardware details like number of bits in a word will also affect a precise empirical graph for a specific processor.
But the overriding conclusion re TF is that the precise optimal level is irrelevant: we are still firepower-limited ATM, and shouldn't bite off more than we can chew.

David

[kladner]

Originally Posted by davieddy

But the overriding conclusion re TF is that the precise optimal level is irrelevant: we are still firepower-limited ATM, and shouldn't bite off more than we can chew.

What you mean "we", paleface?

[davieddy]

Originally Posted by kladner

What you mean "we", paleface?

One of these days, you are going to cop one hell of a scalping mate.

[davieddy]

Originally Posted by davieddy

The time for an LL test is proportional to expo².

Originally Posted by Prime95

Very close:

FFT = n log n
LL = n FFTs = n² log n

If you've ever written a sorting program or FFT, or even summed a geometric series, you will realize how important this ROT is.

Think of a chess board.
8 columns each consisting of 8 squares: 8² squares.
Now suppose we have four columns containing 8,4,2 and 1.
How many squares?

I must refresh myself on the game of Nim!

D

[davieddy]

I spot a niche in the market, and might even get my name in red:

This Primenet monopoly can be broken.
Who needs a single authoratative database?

Oliver has just written a program which makes GPUs TF 100x faster.

I'll recruit as many GPU owners to a private club as I can, and claim as much credit as possible.

Gee! That worked. Look at the GHz days we are churning out.

Bet that wanker Davieddy wished he had this big iron.
He's a bit old, uppity and too smart for comfort though.
Better get him off my back before he exposes what I'm up to.

[davieddy]

Originally Posted by chalsall

For the record, I have grown tired of this game with David.

I have moved all of his recent posts from this thread, and the related replies, to Davieddy's World.

I have no problem with people disagreeing with me -- but at least honest, sincere and logical discussion is expected.

Enough of this pompous crap.

Just face it: you are a bad loser and a jumped up one at that.

Is your "ignore" button not working or something?

[bcp19]

Originally Posted by davieddy

I spot a niche in the market, and might even get my name in red:

This Primenet monopoly can be broken.
Who needs a single authoratative database?

Oliver has just written a program which makes GPUs TF 100x faster.

I'll recruit as many GPU owners to a private club as I can, and claim as much credit as possible.

Gee! That worked. Look at the GHz days we are churning out.

Bet that wanker Davieddy wished he had this big iron.
He's a bit old, uppity and too smart for comfort though.
Better get him off my back before he exposes what I'm up to.

I saw the title and was hoping for something along the lines of Wayne's World, but ended up in an old Odd Couple rerun...

Originally Posted by davieddy

Enough of this pompous crap.

Just face it: you are a bad loser and a jumped up one at that.

Is your "ignore" button not working or something?

I agree, get your pompass crap (mispelling intentional) outta here.

Face it Dave, WE, the users of GPU72 are doing what WE want to do. WE do not tell YOU what to do or how to do it, so give us the same curtesy and butt out.

I don't know why you are blaming Chalsall for setting things up according the wishes of the people using the service he created. He is doing what George either can't (due to programming) or doesn't have the time to do.

Here's a little tidbt for you to sink your teeth into... Due to advances in the software, GPUs no longer tie up 1 or more CPU cores to do their work. Thus your arguement that the CPU cores and GPUs would be better set doing LL than TFing to 74 is so far out in left field that there are polititions wanting you to teach them how to get out that far.

Let's look at a few facts... DC-TF is revisiting areas where we had stopped TF at 69, why? Not cause Chalsall decided to arbitrarily change it, it was changed in response to US, the users, asking for it. Don't bother searching the forum for this, the discussion took place in PMs that I no longer have. I am the DC-TF powerhouse and when I ask for a change, he looks over my suggestions and reasoning and often implements it. Blame: US, the USERS of GPU72.

LMH work... Not something I am interested in, BUT, again, users asked and Chalsall made it work. Blame: US, the USERS of GPU72.

Now on to LL-TF. Yet again, WE the users asked about the bit level changes and it was ecided that yes, we can change them. Yet again, Blame: US, the USERS of GPU72.

Dang, I see a common thread here... Chasall is providing what is asked for after reveiwing the plausibility not laying down the law. Can you get this through your head yet Dave?

You are becoming a TROLL Dave, with nothing productive to add to the conversation, other than some whine about the need to increase computing power to preserve your 4 years between primes theory or some such blather. Go tell AMD and Intel to make better chips and leave those of us working with GPUs to our own devices and stop trying to get us to do things other than what WE want to do. If you feel the project needs more 'firepower' to preserve your theory, you are more than welcome to buy better equipment to help out in that area. Until martial law is decreed and George forbids everything not geared towards finding the next prime, I will do as I dern well please and nothing you do or say will change that.

[Mr. P-1]

Originally Posted by Prime95

P-1: ~5% of the time a factor only saves ~3% of an LL test? Attention P-1ers, are the 5% and 3% accurate estimates?

mprime reports that my chance of P-1 success is about 3.88%. That's lower than it used to be, presumably because of the impact of deeper TF. Since I resumed P-1 on my new computer a couple of months ago, I've returned 216 P-1 results, of which 8 were successful, which is exactly what a 3.88% success probability would have predicted.

I'm not sure how useful this kind of info could be to you. Dedicated P-1ers like myself are not representative of the P-1 effort of the project as a whole. You could probably obtain better statistics from the server.

I couldn't tell you how the time to do P-1 compares with LL since I don't do LLs.