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Old 2017-12-02, 20:34   #1
Dec 2017

3 Posts
Default Some newbie question.

Hi I just download this program and I have few questions.
1) When I start the program the is a line said "Resuming primality test of M47242693 using AVX FFT length 2560k, Pass1=640, pass2=4K, clm=1, 4 threads" What is FFT length and pass mean?
2) and "Iteration: 160000 / 47242693 [0.33%], ms/iter: 4.478, ETA: 58:33:37" Is it mean I finished 160000 out of 47242693 calculation and what is ms/iter: 4.478 mean?
3) In my assessment it said work type "D" is it mean DoubleCheck and what is LL mean?
4)When I click in to the "exponent" I found there are 9 other people done this test before with NF, C and NF-PM1, so am I DoubleCheck this number again, why?
5) Can I get a brand new number to process it?
6) What is worker mean?
7) what is the different between all this: world record test, P-1 factoring, ECM factoring ect...?

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Old 2017-12-02, 21:55   #3
GP2's Avatar
Sep 2003

3·863 Posts

FFT means "fast Fourier transform". It's useful for doing arithmetic more quickly.

The larger the FFT length, the more time it takes to test an exponent. However, larger exponents require larger lengths, because choosing too short a length causes errors. So there is a tradeoff and the program tries to figure out exactly where it needs to transition from one length to another.

Yes, you have finished 160 000 out of 47 242 693 iterations, and it is taking 4.478 milliseconds per iteration on average on your machine. Therefore the estimated time that remains until completion is 58 hours, 33 minutes, 37 seconds.

Yes, you are doing a double check of the Mersenne number M47242693 (which is 247242693 − 1). You are performing a Lucas-Lehmer test, this is an algorithm that determines whether Mersenne numbers are prime or composite.

One other person has done an LL test before. This was on 2009-01-01, and you can see it both at the top and in the History section (the Type "C" result).

However computers are not always reliable, and a single error in all the millions of iterations will cause the result to be wrong. Therefore we do double checks. Historically, the error rate in the first-time LL tests has been 3 or 4 percent on average. This varies greatly, however. Many machines have a perfect or near-perfect record, while a small number are very unreliable.

Before proceeding to do an LL test, we try a shortcut: we attempt to find factors. That is what you see in the history, with the Type "NF" and "NF-PM1" results. The first one refers to "trial factoring" and the second refers to P−1 ("P minus one") factoring. These are just two different methods of trying to find factors.

Obviously, any number that has a known factor is composite, so there is no need to test any further. Note that the LL test determines with certainty whether a Mersenne number is prime or composite, but it does so without finding any factors.

You can abandon the current LL test of M47242693 and get a new assignment. However, there is no reason to do so, because you are doing useful work. If you prefer to do first-time LL tests rather than double checks, you can change your settings to do so. However, these involve larger exponents and will take about four times longer to complete. If you have an older machine, it may be best to stick to double checks.

Modern CPUs have multiple cores, to do work in parallel. So you can have multiple workers working together on an LL test, or they can do multiple LL tests of different Mersenne numbers in parallel.

Currently, the largest known Mersenne prime is M74207281. If you find a larger one, that will be a new world record. All the exponents smaller than 74 207 281 have been tested at least once, so at the moment, in practice there is no difference between asking for ordinary first-time LL test assignments and world-record LL test assignments.

P−1 factoring is just one method of finding factors. It is done before the LL test, and if a factor is found, then we save time because the LL test is now unnecessary.

ECM factoring is another method of finding factors. However, it is not cost-effective to do it before an LL test, because on average it will not save time. If no factor was found by trial factoring or by P−1 factoring, it makes more sense to just proceed directly to LL testing. So ECM factoring is mostly done "just for fun", for exponents that we already know to be composite. It is mostly done by old machines which are too slow to do LL testing (either first-time or double-checking).

Trial factoring is mostly done by graphics cards nowadays (GPUs), which can do this kind of work faster than CPUs.
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Old 2017-12-02, 22:04   #4
VBCurtis's Avatar
Feb 2005
Riverside, CA

130108 Posts

SM88 is a master of wikipedia rather than actual knowledge...

2. Yes. ms/iter = milliseconds per iteration. As you guessed, the program needs to do a calculation the number of times listed in the denominator (which is equal to the exponent you're testing; so bigger exponents require more iterations).

LL means Lucas-Lehmer, the name of the test that determines whether the number is prime. The other listings you found for your number are attempts to factor the number; none of those attempts were successful, so there are no known factors; if a factor was found, we wouldn't need an LL test, since we would know it's composite.

You're doing a double-check because for each number we require two matching results to be sure it's not prime, and we'd like to find out if your computer does reliable computation. If your first result matches one already-completed test, we have good reason to think your machine is "good", and you get first-time work if you request it.

P-1 and ECM are methods to look for factors; they take less time than an LL test, so they're performed by some volunteers who like finding factors rather than doing LL tests. They can't find a prime, as they are methods to find factors (but finding a factor means two LL tests won't be needed, so it helps the project). Until and unless you understand what's going on with the math (by reading the linked wiki articles or the forum, preferably both), you should not consider P-1 or ECM work.

Trial factoring (actually dividing by a bunch of numbers to see if one divides the candidate) is marked TF on the report; in modern times, this work is performed by GPU programs. Forum users have done the mathematics to determine how much of each of these factor-finding methods is optimal for helping the project, while users like you get to actually perform the LL test to find out if the remaining numbers are prime!
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Old 2017-12-03, 04:46   #5
Romulan Interpreter
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Jun 2011

3×23×149 Posts

Originally Posted by GP2 View Post
FFT means...
Very good post! This has to be sticky!
(we should have a FAQ for other people that ask and ask the same questions forever)
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