20101117, 06:25  #1 
Aug 2006
1011011100110_{2} Posts 
Primality proving
I'm sure this is very basic, but where can I find Linux software for proving primality of large general numbers? François Morain's ECPP is limited to about 2000 decimal digits. Pari/GP is happy to attempt a primality proof for large numbers, but its algorithms are not competitive at that size.
Last fiddled with by CRGreathouse on 20101117 at 06:25 
20101117, 06:46  #2 
Bemusing Prompter
"Danny"
Dec 2002
California
2278_{10} Posts 

20101117, 07:16  #3  
A Sunny Moo
Aug 2007
USA (GMT5)
3×2,083 Posts 
Quote:
Numbers as big as 20,562 digits have been proven prime with the FastECPP software distributed over multiple computers, albeit with what appears to be a speciallymodified, notgenerallyavailable version of the program. 

20101117, 14:27  #4  
Account Deleted
"Tim Sorbera"
Aug 2006
San Antonio, TX USA
17·251 Posts 
Quote:


20101117, 15:46  #5  
Bamboozled!
May 2003
Down not across
17×593 Posts 
Quote:
Paul 

20101117, 20:29  #6 
A Sunny Moo
Aug 2007
USA (GMT5)
3×2,083 Posts 
As Paul suggested, a VM could do the trick, though Wine has been used before with success to run Primo on Linux. Gary (a.k.a. gd_barnes) did a large proof for the Five or Bust project that way on one of his Linux boxes and from what I observed the overhead was minimal if at all present. I'm not sure how this compares with a virtual machine, but it was definitely more convenient to set up and use.
Last fiddled with by mdettweiler on 20101117 at 20:29 
20101118, 14:57  #7 
Jan 2008
France
17·31 Posts 
I could indeed get Primo to work with wine.
BTW long ago (~2001) I ran some commandline .exe number crunching program under Wine and they were faster than under Windows. 
20110123, 04:03  #8 
May 2004
New York City
3·1,409 Posts 
Is primo good for primes less than ten million?

20110129, 08:22  #9 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
3^{2}×631 Posts 
For primes that small http://en.m.wikipedia.org/wiki/Mille...primality_test shows what bases need testing for a number to be definitely prime. This should be faster than primo though trial factoring m
ight be faster still. 
20110129, 11:06  #10 
Mar 2007
Austria
2×151 Posts 
For potential prime numbers less than 10^300,PariGP's isprime() function is reasonably fast(altough it doesn't print out a certificate). PariGP runs on linux and you can get it from:
http://pari.math.ubordeaux.fr (or install it via your distribution's package manager) 
20110129, 17:04  #11  
Aug 2006
2×3×977 Posts 
Quote:
It does have the ability to certify primality with isprime(n, 1), though it's very slow. 

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