20120125, 21:31  #1 
Jan 2012
1 Posts 
Fastest software for Mersenne primality test?
What is the fastest software for checking if a Mersenne number is prime? (has to be free/nonbinding, preferably for Windows 64 bit)
Also, approximately how long does checking a 1 billion digit Mersenne prime take? 
20120125, 21:48  #2 
Apr 2010
Over the rainbow
2^{2}·641 Posts 
llravx and aproximately 1 year for current harware.
Last fiddled with by firejuggler on 20120125 at 21:49 
20120125, 22:15  #3 
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}×3×641 Posts 

20120125, 22:24  #4 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
1110000110101_{2} Posts 
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 prizedistribution 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 http://mersenne.org/legal) then try Mlucas or Glucas 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 freegratis). 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 here and here. From the second page: You're looking at around 95,000 GHz days to do one test. One core of my Intel i72600K is able to do ~5 GHzDays per day, that would take me around 50 years. (You could use all four cores, but you'd get less than 15 GHzDays 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 of the exponents. **Note 2: I also just realized that this link from above is not an exponent to be tested, because that link shows it's already been factored. Last fiddled with by Dubslow on 20120125 at 22:31 
20120125, 22:33  #5 
Apr 2010
Over the rainbow
A04_{16} Posts 
cause prime95 v26.6 doesn't support avx?

20120125, 23:23  #6  
If I May
"Chris Halsall"
Sep 2002
Barbados
7×37^{2} Posts 
Quote:
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? 

20120126, 00:01  #7  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Quote:
Last fiddled with by Dubslow on 20120126 at 00:01 Reason: [strike] 

20120126, 00:38  #8  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3^{3}·5·71 Posts 
Quote:
From the wiki: Quote:


20120126, 04:06  #9 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
I actually got around 50 years on one core of my Sandy Bridge.

20120126, 05:57  #10 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
3^{3}·5·71 Posts 

20120126, 18:07  #11 
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Using James' estimate of 95K GHzDays, and assuming I can get 5/day.
http://www.wolframalpha.com/input/?i...+days+to+years Maybe closer to 55 or 60, but still way less than 100. Last fiddled with by Dubslow on 20120126 at 18:09 
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