how are odds computed?

[wblipp]

Originally Posted by crash893

but i think there is a key difference

with gambling you could win once and never win again forever

with primes we know that there are more out there we just dont know how far a part they are.

As Pooh Bear said to Rabbit, "They're the same thing."

You can look at it as "We know there are more box cars to be rolled, we just don't know how far apart they are." Or you can look at it as "although we have a pretty good heuristic, it's possible that we will never find another Mersenne Prime." You can focus on the unlikely "never again" scenario, or you can focus on the "random distance between events" aspect, but both descriptions apply equally well (or equally badly) to BOTH dice rolling and prime hunting.

[cheesehead]

Originally Posted by crash893

as you complete numbers the odds should go up becuase you have elinated canadates.

Here we get confused with saying the odds go "up or "down" or "higher" or "lower".

When you previously wrote "the odds get higher ( less desireable)", you meant (I think) that the odds went from, for example, 1:252,000 to 1:400,000. That can be expressed two opposite ways. You could say the odds went "higher" from 252000-to-1 "up" to 400000-to-1. But you could instead look at the odds as fractions: the odds went "lower" from 1/252000 "down" to 1/400000. It seemed to me you were referring to the many-to-1 view, not the fraction view when you wrote "get higher (less desireable)".

Now, when you write, "as you complete numbers the odds should go up" it seems to me that you are using the fraction view. The fraction's value goes up as its denominator goes down (from 1/252000 to 1/170000, for example). Am I right in thinking that here you're using the opposite view from the one you used earlier?

with gambeling you could win once and never win again forever

Actually, at a legal regulated casino, the games aren't supposed to be rigged to keep you from ever winning again, assuming you have enough patience and stake to keep playing. (But that doesn't mean you'll make a long-term profit.)

with primes we know that there are more out there we just dont know how far a part they are.

No, we don't know that there are more Mersenne primes. (No regulatory agency :-) There are good arguments that they go on forever, but no one has actually proven that.

[markr]

Originally Posted by crash893

its seems to me that you know a prime is going to be in a certian block of numbers
and as you complete numbers the odds should go up becuase you have elinated canadates.

If we knew a prime was going to be in a certain, fixed, block of numbers, then you're right: the odds would keep improving as we eliminate the duds. But hunting primes in unexplored territory is like rolling dice - you just can't tell exactly how many of a particular type will turn up in a game.

In blackjack you have a different situation. You know exactly what cards there are at the start of a game. To some extent it is possible to watch the odds change by counting the cards. Casinos don't like people who do that.

[crash893]

Originally Posted by cheesehead

The simplest way is to let Prime95/mprime choose B1,B2. They will if you use Test= or Pfactor= in the worktodo.ini file.

- - -

If you want to use Pminus1= in worktodo, so that you specify B1,B2 yourself:

Look in the Prime95 help file. Go to "How to use Prime95", then "Setting up available memory". In that section you can find the following table:

Exponent Minimum Reasonable Desirable
6,000,000 12MB 23MB 33MB
10,000,000 19MB 36MB 53MB
33,000,000 65MB 125MB 185MB

Decide whether "Minimum", "Reasonable", or "Desirable" fits your situation, then set your Prime95 available memory number accordingly and remember the category (M/R/D) for the next step.

Next, look in the Pminus1.txt file (after downloading Pminus1.zip and unzipping it). Each line lists an exponent, B1 limit, and B2 limit. Go to where the exponents are similar to the one you want to try factoring. Look at the various B1,B2 combinations that have already been tried for exponents similar to yours.

If your available memory is "Minimum", look for lines where B1 = B2, such as

29922019,435000,435000
29922619,430000,430000

and choose your B1,B2 similar to those.

If your available memory is "Reasonable", look for lines where B2 is roughly 8-12 times as large as B1, such as

29908709,295000,2728750
 
29910631,310000,3487500

and choose your B1,B2 similar to those.

If your available memory is "Desirable" (big), look for lines where B2 is roughly 15-25 times as large as B1, such as

29908399,345000,8711250
 
29909807,330000,6187500
 
29910637,340000,7735000

and choose your B1,B2 similar to those.

You may see "oddball" lines with very small B1 such as

30000041,1000,1000
 
30597587,30,4000000

Such low B1 values mean that P-1 using those limits has very, very little chance of finding a factor. Try them if you want to experiment, but don't hold your breath waiting for a factor.

Among the small exponents you'll see lines with very large B1 (and B2) such as 4290000000. If you want to experiment with those on larger exponents, please just breathe normally ... until you run out of patience waiting for your program to get even 1% done. :)

what i was more going after was that the prime95.exe seems to know the odds from the second you download the workunit

it is not doing any sort of long complex math to do it either so ( or if it is its doing it very quickly)

[wblipp]

Originally Posted by crash893

what i was more going after was that the prime95.exe seems to know the odds from the second you download the workunit.

Sigh.

It's always a disappointment when you try to teach somebody how to think about a problem, but they ignore the new tools you have shown them.

Assuming that you are engaged in a discussion, you have to be arguing that "Odds in prime hunting are different from odds in rolling box cars because ...." In this context, your unstated argument has to be "because its easy to calculate odds in prime hunting and hard to calculate odds in rolling dice."

William

[cheesehead]

Originally Posted by crash893

( or if it is its doing it very quickly)

Yes, computers are fast.

[Mystwalker]

Originally Posted by cheesehead

Yes, computers are fast.

Not everyone - mine hasn't moved at all in the last 2 years! Lame duck...

[crash893]

Originally Posted by wblipp

Sigh.

It's always a disappointment when you try to teach somebody how to think about a problem, but they ignore the new tools you have shown them.

Assuming that you are engaged in a discussion, you have to be arguing that "Odds in prime hunting are different from odds in rolling box cars because ...." In this context, your unstated argument has to be "because its easy to calculate odds in prime hunting and hard to calculate odds in rolling dice."

William

I really dont think there is a need to talk down to anyone here.

[crash893]

Originally Posted by cheesehead

If I read the source code in the commona.c module correctly, the estimate for a first-time LL test of 2^n-1 that has been (unsucessfully) trial-factored to 2^b and P-1 factored to the default limits for exponent n is that it has

1 chance in ( n / ( (b-1) * 1.803) )

of being prime.

E.g., if you're LL testing M29998799 after it's been (unsucessfully) TF'd to 2^67 and P-1'd to B1,B2 = 340000,7650000 or thereabouts, the estimate is about 1:252,000 that it'll be prime.

so is it 1: 29998799/((34000-1)*1.803))

im still confused over the variables in this

also i would like to point out that im not trying to find a pattern or anything like that. i have a programing class and we were told to make a simple program that uses variable ( that the user types in ) and produces a result

[Numbers]

Originally Posted by crash893

so is it 1: 29998799/((34000-1)*1.803))

Not quite. Your 34000-1 interprets cheesehead's b-1, not unreasonably, as meaning B1 minus 1, whereas I think you'll find he meant the level to which it has been trial factored minus 1. So if your number has been trial factored to the 67 bit level (your worktodo.ini file will tell you; the entry will say something like Test=29998799,67,1) then your calculation is 1: 29998799 / ((67-1) * (1.803)) giving you odds of 1: 252094.

[crash893]

Originally Posted by Numbers

Not quite. Your 34000-1 interprets cheesehead's b-1, not unreasonably, as meaning B1 minus 1, whereas I think you'll find he meant the level to which it has been trial factored minus 1. So if your number has been trial factored to the 67 bit level (your worktodo.ini file will tell you; the entry will say something like Test=29998799,67,1) then your calculation is 1: 29998799 / ((67-1) * (1.803)) giving you odds of 1: 252094.

awsome

thanks