Various questions, # of workers - one core HT e.g.

[lorgix]

Hello,

I have a few questions/ideas. I'm hoping to get answers/comments, or get referred to the appropriate already existing thread. Please excuse me if this thread is in the wrong place.


I run a 3.0GHz P4 w. HT. I currently run one worker using both logical CPUs for Prime95 - Prime95 is running two threads.
Question: Would it make any sense running two workers, one for each logical CPU - 2*[1worker:1thread:1logical CPU] on my one physical core?


I like finding factors, somewhat beyond the point that gives the highest frequency of prime identification -
Question: Is there, on this forum, a place for people interested in factoring beyond "optimal" P-1 and/or "optimal" TF?


Question: Do YOU have any recommendations for a person who wants to find any previously unknown factor to any Mersenne number? Essentially finding a factor with as little effort as possible.


I'm looking for an easy way to maximize the chance of finding a factor to a certain number using P-1, by setting optimal B1&B2 given available memory and computational time. So; given available time&memory what bounds gives the highest chance of success?
Question: Could anyone please more or less define this function?


Given that there is enough interest in finding factors (obv. serving the purpose of finding primes as well) and the tremendous effort required to find large factors; triple-checking, or LL-T, should at some point become interesting.
Question: Are there any comments or ideas concerning the concept of LL-T?


Any answers, comments, ideas, references to existing threads or moving this thread to a better place would be appreciated.

[Mini-Geek]

Originally Posted by lorgix

I run a 3.0GHz P4 w. HT. I currently run one worker using both logical CPUs for Prime95 - Prime95 is running two threads.
Question: Would it make any sense running two workers, one for each logical CPU - 2*[1worker:1thread:1logical CPU] on my one physical core?

I don't think so. If so, it'd be a marginal throughput increase. You could always test it out and see if it gives better throughput.

Originally Posted by lorgix

I like finding factors, somewhat beyond the point that gives the highest frequency of prime identification -
Question: Is there, on this forum, a place for people interested in factoring beyond "optimal" P-1 and/or "optimal" TF?

Certainly. This group of subforums is dedicated to factoring, both the search for factors beyond what is optimal for determining primality (especially searching for all factors when the number's compositeness is easy to prove), and projects that search large Mersenne numbers (e.g. 100 million or 1 billion digits) for factors, even though we don't need to do LLs there for a while. Most of the factoring projects don't only focus on Mersenne numbers, but the Cunningham Tables includes Mersenne numbers as part of it (the 2-, i.e. 2^n-1, table). For an easy way to participate in deeper factoring, set Prime95 to request ECM work. ECM is much faster than TF for finding factors beyond the optimal-pre-primality-test level.

Originally Posted by lorgix

Question: Do YOU have any recommendations for a person who wants to find any previously unknown factor to any Mersenne number? Essentially finding a factor with as little effort as possible.

Find a range of very large Mersenne numbers that have been TFd to a relatively low bit level (noting that bit levels get easier on larger numbers, as there are less candidates to search because factors must be 2kp+1). The easiest way to do this, though it won't quite be the fastest way to find an unknown factor, is to request "Trial factoring to low limits" (a.k.a. TF-LMH) from PrimeNet or check out the Lone Mersenne Hunters and LMH > 100M subforums (they're in that Factoring group I linked earlier). To get the easiest work, though, just look at http://www.mersenne.org/report_factoring_effort/ and http://www.mersenne.org/primenet/ and pick your own range (with p less than 1 billion so PrimeNet has it in its DB) and crunch them, then report the results to PrimeNet. Since you'll probably be doing a whole bunch of numbers very quickly, it's best to do this from an instance of Prime95 that is not set to use PrimeNet. It takes a while for it to communicate all of those numbers individually. Instead, grab then numbers from that Factoring Effort page I linked earlier, format them into worktodo.txt format yourself, (set the finishing bit one higher than the current) crunch it, and then give PrimeNet the results at http://www.mersenne.org/manual_result/. You can also check out LMH's instructions. You might want to do it more like they do than what I said, (pretty similar...you might just find it easier to follow those directions) your choice.

Originally Posted by lorgix

I'm looking for an easy way to maximize the chance of finding a factor to a certain number using P-1, by setting optimal B1&B2 given available memory and computational time. So; given available time&memory what bounds gives the highest chance of success?
Question: Could anyone please more or less define this function?

The higher the B1 and B2, the higher the chance of finding a factor. The more memory you give it, the faster it can run stage 2 (at least I think that's how that works...). I don't know how you'd calculate what bounds to pick to make it take a specified time with a specified amount of memory. It might be easiest to just try telling it a few bounds (Advanced > P-1) and see how long it says it will take (Test > Status). For knowing what B2 to choose, relative to B1, they ought to take about the same time to be optimal (IIRC).

Originally Posted by lorgix

Given that there is enough interest in finding factors (obv. serving the purpose of finding primes as well) and the tremendous effort required to find large factors; triple-checking, or LL-T, should at some point become interesting.
Question: Are there any comments or ideas concerning the concept of LL-T?

When two LLs have matching residues, there is about a 1 in 2^64 chance that at least one of them is wrong. The chances that two LLs with matching residues will say a number is composite when it's really prime are even lower. There is no reason to triple-check. The LL test only tells you if a number is composite or prime, not anything about its factors.
Besides, by the time you're interested in finding the full factorization of a number, proving that it's composite should be relatively trivial. Factoring is far harder than proving that a number is composite, especially for Mersenne numbers.

[cheesehead]

Originally Posted by Mini-Geek

There is no reason to triple-check.

Sure, there is. We've found errors in past results several times throughout the GIMPS project. Running triple-checks can also be a good way of determining whether a new system is reliable. I'd agree that it's not a mainstream concern of GIMPS, or a PrimeNet-assignable task, to triple-check, though.

Some folks (Brian Beesley is the best-known to me) actually did triple-check all the results for all low exponents (up to somewhat past 1M IIRC) that hadn't yet had two 64-bit residues recorded. (David Slowinski's residues were no longer than 14 bits.) There've even been quadruple-checks recorded -- perhaps from check-outs of new systems, as suggested above. Check the "LL Results" or "Exponent Status" report below and around 1M for examples.