Davieddy's World

[davieddy]

Originally Posted by Aramis Wyler

Technically, it would be 44% more work in 93% of the time. But you could say the same for factoring two of them from 69 to 70 instead of taking them from 69 to 71. There are always diminishing returns going up a bitlevel, but we try to get as close as we can to optimal
with the firepower we have.

Expected LL work saved TFing 1 expo from 71 to 75 is 4/75
Expected LL work saved TFing 2 expos from 71 to 74 is 6/74 (over 50% more).

Don't miss the wood for the trees. Don't miss simple points of principle by being over-pedantic with precision. One of the faults of many folk here in my world.

D

D

[Chuck]

Originally Posted by Aramis Wyler

I have good news though! We'll have more gpu power working on factoring in just a few weeks when the DCTF runs out. Currently My and Chuck's daily output on DCTF is higher even than Pete's (though we'll never catch up to the work he did) and then that should all go to LLTF.

I did the DCTF work the past few days just for a lark — I normally don't work that range but rather the "let GPU72 decide". I have just added a second GTX690 obtained used from a member of this forum.

[Aramis Wyler]

Expected LL work saved TFing 1 expo from 71 to 75 is 1/72+1/73+1/74+1/75 = .054
Expected LL work saved TFing 2 expos from 71 to 74 is 2*(1/72+1/73+1/74) = .082 (44% more).

I have no real need to be imprecise when I'm sitting in front of a computer. I thought the difference between 50% (now even more) and 44% was worth clarifying since I was, you know, parked in front of a giant calculator and using it to post on the forum.

I was not arguing though, just clarifying. There are diminishing returns either way.

[R.D. Silverman]

Originally Posted by Aramis Wyler

Expected LL work saved TFing 1 expo from 71 to 75 is 1/72+1/73+1/74+1/75 = .054
Expected LL work saved TFing 2 expos from 71 to 74 is 2*(1/72+1/73+1/74) = .082 (44% more).

WRONG!

Why do I say wrong? I will offer a hint in the form of a question:
Is the probability of finding a factor between 71 and 72 bits
INDEPENDENT of the probability of finding one less than 71 bits???

Further hint: Among those number that have a factor between 71 and 72
bits are some who have a factor smaller than 71 bits.

This entire thread is full of nonsense from many parties. It is devoid
of information content and has a number of posters behaving like
spoiled and ignorant school children. Tis. Tis'nt. Tis. Tis'nt........

And anyone who thinks that increasing TF from (say) 73 to 74 bits
is actually going to increase the rate at which GIMPS finds primes, I say
you are deluded.

These attempts at "optimization" are simply lost in the noise of the overall
process. And it really DOESN'T MATTER. GIMPS moves along
regardless. And whether the next prime is found in (say) 15 months or
whether it takes 16 months is UNIMPORTANT.

Unless of course one is an anal-retentive member of the IGG.

[firejuggler]

Originally Posted by R.D. Silverman

WRONG!


Further hint: Among those number that have a factor between 71 and 72
bits are some who have a factor smaller than 71 bits.

yes but those exponent which have a factor below 71 bit WON'T be taken to 73 or 74 bit; and won't be LL'ed.

[R.D. Silverman]

Originally Posted by firejuggler

yes but those exponent which have a factor below 71 bit WON'T be taken to 73 or 74 bit; and won't be LL'ed.

Sigh.

When is it legitimate to add the probabilities????

[swl551]

Originally Posted by R.D. Silverman

Sigh.

When is it legitimate to add the probabilities????

In horseshoes and hand grenades?

[davieddy]

Originally Posted by Aramis Wyler

Expected LL work saved TFing 1 expo from 71 to 75 is 1/72+1/73+1/74+1/75 = .054
Expected LL work saved TFing 2 expos from 71 to 74 is 2*(1/72+1/73+1/74) = .082 (44% more).

I have no real need to be imprecise when I'm sitting in front of a computer.

Your computer is drunk: .082/.054 = 1.52
You are drunk: the probability of one or more factors between 71 and 74 (assuming independence) is 1 - (71/72)*(72/73)*(73/74) = 3/74

(6/74)/(4/75) = 1.52

Originally Posted by R.D. Silverman

And anyone who thinks that increasing TF from (say) 73 to 74 bits is actually going to increase the rate at which GIMPS finds primes, I say you are deluded.

Ah yes I see it now: 74 LL tests will take the same time as 73.

David

[science_man_88]

Originally Posted by davieddy

the probability of one or more factors between 71 and 74 (assuming independence) is 1 - (71/72)*(72/73)*(73/74) = 3/74

see I don't see how we can have independence since k=1 being eliminated eliminates k=2p+2 for example.

[davieddy]

Originally Posted by R.D. Silverman

Sigh.

When is it legitimate to add the probabilities????

When you want the probability of one of a number of mutually exclusive possible outcomes occurring?
Archery is a classic example.
Or probability distributions in general.
Apart from these esoteric examples, addition would seem to be not worth learning about.

[R.D. Silverman]

Originally Posted by davieddy

When you want the probability of one of a number of mutually exclusive possible outcomes occurring?
Archery is a classic example.
Or probability distributions in general.
Apart from these esoteric examples, addition would seem to be not worth learning about.

Clueless.
He ADDED four probabilities. But they were NOT independent!