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-   -   Fastest software for Mersenne primality test? (https://www.mersenneforum.org/showthread.php?t=16474)

JonathanM 2012-01-25 21:31

Fastest software for Mersenne primality test?
 
What is the fastest software for checking if a Mersenne number is prime? (has to be free/non-binding, preferably for Windows 64 bit)

Also, approximately how long does checking a 1 billion digit Mersenne prime take?

firejuggler 2012-01-25 21:48

llravx and aproximately 1 year for current harware.

cheesehead 2012-01-25 22:15

[QUOTE=firejuggler;287231]llravx[/QUOTE]Oh? How does llravx run faster than prime95 when testing a Mersenne number?

Dubslow 2012-01-25 22:24

LLR tests Mersenne numbers?

Prime95 is the fastest as far as x86 processors go, and it is mostly free, except that if you discover a prime with it, you must abide by the Great Internet Mersenne Prime Search prize-distribution rules (you'll get a third of the EFF prize for a 100M digit prime, or a few thousand dollars or so for just a 'regular' prime).

If even that is too much of a restriction (it isn't really, I encourage you to read [url]http://mersenne.org/legal[/url]) then try [url=http://mersenne.org/freesoft/mlucas.html]Mlucas[/url] or [url=http://oxixares.com/glucas/]Glucas[/url] which are programmed in Fortran and C respectively (as opposed to x86 Assembly for Prime95). I am unsure about their license terms, though if I had to guess I'd say they're free (as in freedom, and definitely free-gratis).

Prime95 includes 64 bit optimizations, although they're not really significant for LL tests.

As for a billion digit number, I highly recommend you give up any hope of testing it with any program available. It will be impossible for (AT LEAST) the next 20 years. For more details, see [url=http://mersennewiki.org/index.php/Operation_Billion_Digits]here[/url] and [url=http://mersenne-aries.sili.net/exponent.php?exponentdetails=3321928097]here[/url]. From the second page: You're looking at around 95,000 GHz days to do one test. One core of my Intel i7-2600K is able to do ~5 GHz-Days per day, that would take me around 50 years. (You could use all four cores, but you'd get less than 15 GHz-Days per day, because the LL test isn't very well parallelizable).

*Note: It also just occurred to me that Prime95 (and presumably the other testing programs) can't even test numbers that are a billion digits long. The maximum Prime95 exponent is 596M, whereas the lowest prime exponent that produces a billion digits is 3,321M. Note the order of magnitude difference [i]of the exponents[/i].

**Note 2: I also just realized that [url=http://mersenne-aries.sili.net/exponent.php?exponentdetails=3321928097]this link[/url] from above is not an exponent to be tested, because that link shows it's already been factored.

firejuggler 2012-01-25 22:33

cause prime95 v26.6 doesn't support avx?

chalsall 2012-01-25 23:23

[QUOTE=Dubslow;287237]Prime95 is the fastest as far as x86 processors go, and it is mostly free, except that if you discover a prime with it, you must abide by the Great Internet Mersenne Prime Search prize-distribution rules (you'll get a third of the EFF prize for a 100M digit prime, or a few thousand dollars or so for just a 'regular' prime).[/QUOTE]

Let us run a thought experiment...

Imagine that someone can factor really quickly... Perhaps by using Quantum Uncertainty...

And imagine that a few thousand dollars or so was small change.

Would they advertise that ability?

Dubslow 2012-01-26 00:01

[QUOTE=Dubslow;287237]
Prime95 is the fastest as far as x86 processors go, and it is mostly free, except that if you discover a prime with it, you must abide by the Great Internet Mersenne Prime Search prize-distribution rules (you'll get a third of the EFF prize for a 100M digit prime, or a few thousand dollars or so for just a 'regular' prime). [/QUOTE]

***Note 3: As far as [strike]anyone[/strike] the public knows.

Uncwilly 2012-01-26 00:38

[QUOTE=JonathanM;287227]What is the fastest software for checking if a Mersenne number is prime? (has to be free/non-binding, preferably for Windows 64 bit)

Also, approximately how long does checking a 1 billion digit Mersenne prime take?[/QUOTE]

[QUOTE=firejuggler;287231]llravx and aproximately 1 year for current harware.[/QUOTE]Basically nothing handles LL testing of numbers that large. And it would take too long.
From the [URL="http://www.mersennewiki.org/index.php/Operation_Billion_Digits"]wiki[/URL]:[QUOTE]There isn't hope of really finding such a prime with today's technology and algorithms. A Lucas-Lehmer primality test is estimated to require 852 years.[/QUOTE]

Dubslow 2012-01-26 04:06

I actually got around 50 years on one core of my Sandy Bridge.

Uncwilly 2012-01-26 05:57

[QUOTE=Dubslow;287260]I actually got around 50 years on one core of my Sandy Bridge.[/QUOTE]What FFT size are you setting it for?

Dubslow 2012-01-26 18:07

Using James' [URL="http://mersenne-aries.sili.net/exponent.php?exponentdetails=3321928097"]estimate[/URL] of 95K GHzDays, and assuming I can get 5/day.
[url]http://www.wolframalpha.com/input/?i=95000%2F5+days+to+years[/url]
Maybe closer to 55 or 60, but still way less than 100.


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