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 2010-09-03, 12:37 #1 RichardB   Apr 2010 England 1410 Posts What will happen? If it says I'm at 55% then what is that? calculating the number? checking if it's prime?
 2010-09-03, 14:14 #2 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 10000101011112 Posts Calculating the number is easy. Finding factors or proving if the number is prime or composite is hard. As for what your computer is actually doing that it's at 55%, I can't tell you without more information. There are a few different tests Prime95 uses: a few short tests of TF (trial factoring) and P-1 (another way to find factors, runs a stage 1 and a stage 2) that try to eliminate the number without running the long test: the LL (Lucas-Lehmer) test that proves whether the number is prime or composite. The LL test must run all the way to 100% before the result is known at all. It's not like factoring that can stop any time if it finds a factor. If you're interested in more about the math and tests behind GIMPS, see http://www.mersenne.org/various/math.php
 2010-09-03, 14:17 #3 RichardB   Apr 2010 England 2·7 Posts Thanks, this is what it says exactly: [Worker #1 Sep 3 14:59] Iteration: 27740000 / 49613569 [55.91%]. Per iteration time: 0.096 sec. [Worker #2 Sep 3 15:04] Iteration: 28190000 / 49661327 [56.76%]. Per iteration time: 0.087 sec. Edit after reading webpage: I think I understand how it works and why iterations are mentioned. If a mersenne is supposedly found are there more checks? A traditional odd factor check? Last fiddled with by RichardB on 2010-09-03 at 14:33
2010-09-03, 15:38   #4
Brian-E

"Brian"
Jul 2007
The Netherlands

2×3×5×109 Posts

Quote:
 Originally Posted by RichardB Thanks, this is what it says exactly: [Worker #1 Sep 3 14:59] Iteration: 27740000 / 49613569 [55.91%]. Per iteration time: 0.096 sec. [Worker #2 Sep 3 15:04] Iteration: 28190000 / 49661327 [56.76%]. Per iteration time: 0.087 sec. Edit after reading webpage: I think I understand how it works and why iterations are mentioned. If a mersenne is supposedly found are there more checks? A traditional odd factor check?
The extra information you give makes it clear that these are LL-tests of two separate mersenne numbers, so what Mini-Geek wrote about Lucas-Lehmer testing is relevant for you.
Should either number turn out to be prime, you can be sure that your positive result would immediately be checked by at least two independent trusted members of the GIMPS community on fast dedicated hardware. It would still take a few weeks to verify. This testing will simply be a re-run of your own LL-test.

You can probably see that looking for factors would be pointless in this situation: if your test was correct there aren't any other than 1 and the mersenne number itself, and testing all possible factors (even though only certain special numbers of the form 2kp+1 can possibly be factors - where p is your exponent) is clearly impossible since the mersenne number being tested is astronomical in size.

If the double-checking LL-tests confirm the primality, there is no doubt that the number is prime.

 2010-09-03, 15:55 #5 RichardB   Apr 2010 England 2×7 Posts Thanks. One more question- do we check all the prime exponents? I just ran my own prime finding program from 40000000 to 60000000 (to find my exponents), there are 1000s to check. It seems incredible we've checked all the ones below in the time we have.
 2010-09-03, 18:14 #6 Primeinator     "Kyle" Feb 2005 Somewhere near M52.. 16238 Posts No. The numbers being tested are solely for the form 2^p -1, where p is a prime number. We HAVE tested all numbers of this form for values of p close to 21.5 million. However, there is a nearly unfathomable amount of primes not of the form 2^p -1 that have not been tested. In fact, with our methodology, it is not possible to test these numbers. Hope this helps!
 2010-09-03, 19:28 #7 RichardB   Apr 2010 England 2×7 Posts If we've only done up to 21.5M why is my exponent 49M?
2010-09-03, 19:30   #8
Brian-E

"Brian"
Jul 2007
The Netherlands

CC616 Posts

Quote:
 Originally Posted by Primeinator No. The numbers being tested are solely for the form 2^p -1, where p is a prime number. We HAVE tested all numbers of this form for values of p close to 21.5 million.
Of course you're talking about numbers which have their primeness/compositeness firmly established with two independent matching LL-tests (or a factor found) whereas I think RichardB is referring to first-time LL-testing.

If I understand correctly, then almost all unfactored mersenne numbers with exponent up to around 38 million have been LL-tested at least once. After that it's a sliding scale up to the leading edge just under 50 million with some tests completed and some still outstanding.

To RichardB: yes, I think it's amazing too that so much has been tested. Clearly the result of a well-organized project which has been running for some 14 years with thousands of well co-ordinated volunteers. Though remember that for many mersenne numbers with prime exponents a factor can be quickly found so that a lengthy LL-test is unnecessary. For a large proportion of the mersenne numbers this factor is small and is found almost at once.

2010-09-03, 19:38   #9
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

4,271 Posts

Quote:
 Originally Posted by Primeinator No. The numbers being tested are solely for the form 2^p -1, where p is a prime number.
He specified "prime exponents". Your statements are accurate, but directed wrong.
Quote:
 Originally Posted by RichardB Thanks. One more question- do we check all the prime exponents? I just ran my own prime finding program from 40000000 to 60000000 (to find my exponents), there are 1000s to check. It seems incredible we've checked all the ones below in the time we have.
Yes. Just to clarify what I think you're saying, you mean that for every prime p up to where you're at we've checked if 2^p-1 is prime, correct? In other words, that we check every prime exponent along the way. This is mostly correct: We've at least started work on all of them, though not all are done. And as Primeinator said, we've fully checked and double checked up to about 21.5M (precisely: all below 21,065,063 have been double checked and all below 31,494,937 have been checked once, as it says on this page). The reason that most work (like yours) is so far ahead of these milestones is a tail end effect: everything from 21.5M-49M is being worked on. Some computers take months, some tests are bad so a third test has to be run, etc. This means that the 100% full checks of whole areas takes quite a long time, and runs far behind the leading edge of assignments.
But the task isn't as monumental as it seems, since less than half of the numbers make it through all the factor checks. (see http://www.mersenne.org/primenet/ and compare Range Count, the number of primes in that range, to Composite F, the number with factors) Most of those factors are found within minutes of work. There are also a LOT of CPUs working on it. Yes, there are thousands of numbers to check, but if thousands of CPUs work together, you can finish it in a reasonable time. Since each number is considered separately, this sort of parallelization is trivially easy.

Last fiddled with by Mini-Geek on 2010-09-03 at 19:39

 2010-09-03, 20:12 #10 RichardB   Apr 2010 England E16 Posts Thanks a lot Mini Geek, Brian-E and Primeinator, all my questions have been answered very well :) This community really is incredible. I'd love to add my new MacBook Pro to the effort (for basic checks only) but I have a problem I wouldn't want to complicate, same forum: http://www.mersenneforum.org/showthr...290#post228290
2010-09-03, 20:31   #11
mdettweiler
A Sunny Moo

Aug 2007
USA (GMT-5)

141518 Posts

Quote:
 Originally Posted by RichardB I'd love to add my new MacBook Pro to the effort (for basic checks only) but I have a problem I wouldn't want to complicate, same forum: http://www.mersenneforum.org/showthr...290#post228290
While I'm afraid I don't have a clue as to the cause of the extra computer showing up on your account, I can say with reasonable surety that adding another computer probably won't complicate the problem at all. So I'd go ahead and add the MacBook right away.

One thing to keep in mind, though, when crunching on a laptop: it's imperative that the laptop is positioned properly for optimal cooling, otherwise it can get REALLY hot with the CPU running full tilt for an extended period of time. (This could lead to thermal throttling, which can seriously impact your computer's crunching speed--and possibly even make normal operation a little more sluggish.) A couple tips:

-Leave the laptop lid open. Much of the heat radiates up through the keyboard, so it's better to have that area open rather than have the heat hit the lid and bounce around the laptop's chassis for a while before finally making its way out the bottom.

-The more airflow under the laptop and behind it, the better. There are expensive cooling pads you can buy to stick your laptop on, but a much cheaper way is to just use a basic cooling rack from your kitchen.

-Most importantly, make sure that the fan(s) (usually on the back, but sometimes on the sides) are not blocked.

-And last but not least: I'd recommend that you only crunch when the laptop is plugged in. Otherwise, it will drain the battery a lot faster than normal, which kind of defeats the purpose of running on battery. I believe Prime95 has a built in option that, when enabled, detects when it's running on battery and stops crunching until you plug it back in.

Hope this helps!

Last fiddled with by mdettweiler on 2010-09-03 at 20:31 Reason: typo

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