Musing on TF limits

davieddy · 2012-12-01, 06:47

Suppose TFing one more bit has a 1/N chance of finding a factor.

Conventional wisdom says that if an LL test on the same processor takes the same time as N TFs, you toss a coin to decide whether or not to do the extra bit.

I say that doing the extra bit is clearly best.

Not only is finding a factor better than "proving" composite, but every exponent for which no factor is found has its probability of being prime boosted by a factor of (1+1/N).

D

LaurV · 2012-12-02, 12:50

Ok, I agree.
You do the first hundred expos.
From 73 to 74 bits.
Then we talk...

garo · 2012-12-02, 14:17

We are already doing that. Have you looked at James's optimal GPU TF limits page? Get with the program!

Uncwilly · 2012-12-02, 15:13

Quote:

Originally Posted by LaurV

Then we talk...

Quote:

Originally Posted by garo

Get with the program!

Quote 2

LaurV · 2012-12-03, 02:23

Quote:

Originally Posted by Uncwilly

"wrestling with a pig"

Exactly that I was thinking about, but I did not know the English expression. Thanks for the link. David is doing only LL anyhow, and is in his best interest to get exponents TF-done as high as possible, 200 bits if someone else would do the work. This increases his chances to find a prime, without doing any "dirty" work as TF-ing, and meantime we "waste" our time and chances, because we use the resources to TF instead of LL (which in turn, increase his chances more, of course!

). We have a saying, "let the stupids beat (skim?) the milk, I eat the cream", or something like that, can't translate it exactly. It is indeed very "trollish" from him to come with that proposal, especially when everybody knows he is only doing LL (he said it many times). Therefore the "you do the first hundred, then we talk". I did not try to feed any trolls, but to scare them off...

Uncwilly · 2012-12-03, 02:43

This Heinleinism might be useful as well.

Batalov · 2012-12-03, 04:12

How about the one about lipstick?

davieddy · 2012-12-03, 05:45

Will someone please engage their brain and grasp the point I was making in my OP.

FWIW 73 bits is the appropriate limit ATM because TF is doing ~350 expos a day between 60 and 61M. If the LL wave keeps pace (AND I'LL TELL YOU HOW THIS CAN BE ACHIEVED), the expected time to the next prime will be 4 years. This requires the wave to advance by 10% per year,
and so the increased computing required should be forthcoming.

David (who CAN see the wood for the trees).

LaurV · 2012-12-03, 06:24

The only association between the pigs and lipstick I can think about is a very old (and very good) article of Gary North, titled "Lipstick on Bernanke's Pig", there must be some free copies around (I am subscribed to his daily reckon).

edit: found a link

Batalov · 2012-12-03, 07:29

Is it really that hard?

Not to mention, of course:

davieddy · 2012-12-04, 18:43

Quote:

Originally Posted by garo

We are already doing that. Have you looked at James's optimal GPU TF limits page? Get with the program!

What is it that you are immediately

doing?

I have been well ahead of the "program" for years.

Get my post restriction lifted and I will be able to respond more promptly and clearly.

D

2012-12-01, 06:47	#1
davieddy "Lucan" Dec 2006 England 1100101001010₂ Posts	Musing on TF limits Suppose TFing one more bit has a 1/N chance of finding a factor. Conventional wisdom says that if an LL test on the same processor takes the same time as N TFs, you toss a coin to decide whether or not to do the extra bit. I say that doing the extra bit is clearly best. Not only is finding a factor better than "proving" composite, but every exponent for which no factor is found has its probability of being prime boosted by a factor of (1+1/N). D

2012-12-03, 05:45	#8
davieddy "Lucan" Dec 2006 England 2×3×13×83 Posts	Sticks, stones and enemas Will someone please engage their brain and grasp the point I was making in my OP. FWIW 73 bits is the appropriate limit ATM because TF is doing ~350 expos a day between 60 and 61M. If the LL wave keeps pace (AND I'LL TELL YOU HOW THIS CAN BE ACHIEVED), the expected time to the next prime will be 4 years. This requires the wave to advance by 10% per year, and so the increased computing required should be forthcoming. David (who CAN see the wood for the trees).

2012-12-03, 06:24	#9
LaurV Romulan Interpreter Jun 2011 Thailand 2⁶·151 Posts	The only association between the pigs and lipstick I can think about is a very old (and very good) article of Gary North, titled "Lipstick on Bernanke's Pig", there must be some free copies around (I am subscribed to his daily reckon). edit: found a link Last fiddled with by LaurV on 2012-12-03 at 06:26

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2012-12-02, 12:50	#2
LaurV Romulan Interpreter Jun 2011 Thailand 2⁶·151 Posts	Ok, I agree. You do the first hundred expos. From 73 to 74 bits. Then we talk...

2012-12-02, 14:17	#3
garo Aug 2002 Termonfeckin, IE 101011001100₂ Posts	We are already doing that. Have you looked at James's optimal GPU TF limits page? Get with the program!

2012-12-03, 02:43	#6
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2²×23×107 Posts	This Heinleinism might be useful as well.

2012-12-03, 04:12	#7
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	How about the one about lipstick?

2012-12-03, 07:29	#10
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Is it really that hard? Not to mention, of course: