Probabilistic optimization of P-1 efforsts?

[Gordon]

Originally Posted by ewmayer

Most common objective function is 'for a given compute effort, maximize our odds of success.' Effort can be measured in various ways, either raw CPU-cycles, wall-clock time or - for the enviro-conscious crowd - watt-hours, but once those considerations have been turned into compute hardware, it all boils down to the same thing, getting maximum utitlity ('successes') out of same. For GIMPS p-1 work, our success metric is 'given a large set of moduli M(p) and a given compute effort, maximize the % of M(p) for which p-1 finds a factor.' That of course needs to be balanced against the other work types (TF, LL, also ECM for smaller moduli), but within the p-1 effort we want to simply want to maximize our odds of finding a factor for a given compute effort.

For p-1 stage 1 the compute effort is linear in the bitlength of the stage 1 small-primes product, thus we want our product of primes <= B1 to maximize the odds of capturing the primes <= B1 in one or more of the factors of the modulus in question. As you point out in post #2 (for N of no special form), "The probability that an integer N is divisible by p^k, is very nearly 1/p^k", thus the kind of small-prime-powers scheme Tom Womack laid out in #4 is optimal, or as close as we are likely to get given the granularity of the powers involved. If you have a nontrivially-better scheme for constructing a stage 1 primes product, by all means shout it from the rooftops! Do you?

For moduli with factors of special form like our beloved M(p) we may need to make slight modifications to the above schema - M(p) have factors of form 2.k.p+1, so p-1 guaranteed to be divisible by the prime exponent, thus we make sure to 'salt' the stage 1 primes product with p if our overall stage 1 bound B1 is less than p.

But you know all this already, thus I assert you are simply being a trollish, argumentative twit because such is your nature, as demonstrated in-depth in literally hundreds of threads on this forum. You appear to be the only one who thinks your behavior in this (and similar) threads is perfectly reasonable. Luckily you are not the arbiter of what constitues acceptable standards of discourse here.

[science_man_88]

Originally Posted by R.D. Silverman

What does it mean (in your view) for one method to work better than another?
One can choose parameters to give a higher probability of success. But it will run slower....
Is this better? The probability will not increase linearly with the run time.

This is the heart of the whole discussion. Specify an objective function (or other metric)
that let's us decide what "works better" means.

the one's that eliminate as many k as possible that are already deemed possible ? properties of k values producing 2kp+1 that can work depend on things about p and then we can pick what works best to eliminate the rest with the fewest repeats ?

[R.D. Silverman]

Originally Posted by ewmayer

M

But you know all this already, thus I assert you are simply being a trollish, argumentative twit because such is your nature, as demonstrated in-depth in literally hundreds of threads on this forum. You appear to be the only one who thinks your behavior in this (and similar) threads is perfectly reasonable. Luckily you are not the arbiter of what constitues acceptable standards of discourse here.

You are one fucking piece of shit asshole. NOTHING, repeat NOTHING I have said in this
thread is anything close to a flame. But you reply with namecalling: " trollish, argumentative twit"

Nothing anyone has said in this thread has come even close to specifying an optimization problem.
I thought you would have the background and intelligence to see this. I can see that I was wrong.

Who the fuck appointed YOU arbiter of reasonable behavior? Based on your many threads in the
political sub-forum you seem to have a total dislike, distrust and hatred of everything the
government of your adopted country does. I've observed your hatred toward U.S> policy
for years. You NEVER have anything nice to say.
You post nothing except diatribe against the U.S. and its government.
And you conducted one hell of a flame war with cheesehead for YEARS.

And you appoint yourself judge of MY behavior in this thread???

Go back to where you came from. Fuck off.

[LaurV]

Grrr.. a lot of pride here around, just when I was starting to like this topic...

Can some mod close the thread please? Everything need to be said was said, both of you are partially right and partially wrong. That's enough.

[xilman]

Originally Posted by LaurV

Grrr.. a lot of pride here around, just when I was starting to like this topic...

Can some mod close the thread please? Everything need to be said was said, both of you are partially right and partially wrong. That's enough.

Done.