20110201, 11:29  #1 
Jan 2010
1110010_{2} Posts 
Decimal Value of Mersenne Prime
I have an assembly program to calculate the actual value of a Mersenne Prime, given the exponent: start with 1, [double and add 1], ad libitum. IIRC it takes over a day on a single thread of a Core 2 Duo to produce the current largest Mersenne Prime.
Could that calculation be sped up appreciably using CUDA? (Or some other formula)? Cheers. 
20110201, 12:37  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×11×421 Posts 
mpz_pow()
mpz_out_str() ? 
20110201, 13:26  #3 
Tribal Bullet
Oct 2004
2·3·19·31 Posts 
There are fast base conversion algorithms that make this process easy, assuming fast largeinteger multiplication (see volume 2 of Knuth). I would think that for a 12million digit number you could finish in less than a second.

20110201, 15:47  #4 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
23F5_{16} Posts 
Mprint does it very fast. I could not find an active link to the proper website, so I will attach it.

20110201, 18:15  #5  
Jun 2003
10010010001_{2} Posts 
Quote:
Last fiddled with by Mr. P1 on 20110201 at 18:16 

20110201, 22:20  #6 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×11×421 Posts 
http://en.wikipedia.org/wiki/Exponen...ring_algorithm
...but of course mpz_pow() simply does that for you. 
20110201, 23:41  #7  
"Robert Gerbicz"
Oct 2005
Hungary
1,429 Posts 
Quote:
What is not in wikipedia article, that in some cases you can compute the power in linear time, for example the power 2^p. Say you want to compute b^k, then gmp first searches the number of trailing bits of b, let this e, then b=2^e*u, where u is odd, and b^k=u^k*2^(e*k), this means that you need to compute *only* u^k then by an easy shift you can get b^k. If you apply this for the computation of 2^p then you will get this it in (optimal) linear time. ps. obviously after the powering you need a mpz_sub_ui() also to get 2^p1 Mersenne prime. Last fiddled with by R. Gerbicz on 20110201 at 23:45 

20110202, 00:21  #8  
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
Quote:


20110202, 00:57  #9 
Tribal Bullet
Oct 2004
2×3×19×31 Posts 
The OP wanted to compute the decimal value of a Mersenne prime to full precision (millions of digits).
Even if you were a whiz with asm, you will not get his algorithm the thousands of times speedup to compete with using a better algorithm in the first place. 
20110202, 01:40  #10 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
well if it could be extended I'd suggest f2xm1 as it calculates Mersenne numbers directly, by the sounds of it.

20110202, 01:48  #11 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
10010000101110_{2} Posts 
There's more than one way to skin a cat (e.g. trade base conversion for instead computing in an array of base 10^{9} 'digits'), but ... because the threeliner GMPC program only takes a few seconds who would want to spend more time writing a custom program?
>R. Gerbicz: yes, of course, you're right. There's an interesting google find about mpz_pow() absense (as a literal semantic) ... and some of us even know who Digital Parasite is. 
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