20050210, 14:32  #1 
Nov 2004
10_{10} Posts 
Is Mathematica really slow?
M[p_]:=2^p1
LL[p_]:=Module[{s,c,counter}, If[PrimeQ[p]==False,Print["The exponent must be prime"]]; s=4; c=M[p]; counter=0; iter=p1; Print["Iteration : 0 "," / ",iter]; For[i=1,i<iter,i++, s=Mod[s^22,c]; counter++; If[Mod[counter,10^3]==0,Print["Iteration : ",counter," / ",iter]] ] If[s==0,Print["is prime"],Print["is not prime"]] ] ' Test run '  LL[11119]//Timing Iteration : 0 / 11118 Iteration : 1000 / 11118 Iteration : 2000 / 11118 Iteration : 3000 / 11118 Iteration : 4000 / 11118 Iteration : 5000 / 11118 Iteration : 6000 / 11118 Iteration : 7000 / 11118 Iteration : 8000 / 11118 Iteration : 9000 / 11118 Iteration : 10000 / 11118 Iteration : 11000 / 11118 " is not prime" {15.112 Second,Null} Hello, I was experimenting with Mathematica v5.0 about the Lucas_Lehmer test. As you can see above the code is extremely slow. It needs 15+ sec to test the exponent where as Prime95 only takes about 0.5 sec. Can someone explain why is this happening because as far as I am concerned Mathematica is believed to be one of the fastest numerical computing platforms. Any help would be grateful. 
20050210, 14:49  #2 
Jul 2004
Potsdam, Germany
3·277 Posts 
I remember that Louis Helm (one of the creators of SoB  which uses the same algorithmic implementation as Prime95) once said that an implementation in Java would be roughly 30 times slower.
I think the reason here is similar: The speed difference (incidently 30 times as well) supposely comes from the fact that Mathematica's routines are not handoptimized for this exact purpose and architecture (does Mathematica use SSE2/FFTs/IBDWT?). In addition, I believe some "tricks" prime95 uses can only be applied due to special properties of mersenne numbers. Mathematica can't take that into account, I guess. Last fiddled with by Mystwalker on 20050210 at 14:52 
20050210, 20:51  #3 
Dec 2003
Hopefully Near M48
2·3·293 Posts 
Mathematica is slow in other things too. It took Mathematica hours to compute just 25,000 digits of Zeta(3). Other programs can do it in a fraction of a second on the same computer.

20050210, 23:16  #4 
Jan 2005
Transdniestr
503 Posts 
Is Maple faster in general?

20050211, 01:45  #5 
Nov 2004
2×5 Posts 
Thanks anyway for your replies.
I am trying to comprehent the deeper things apon LL, that experiment showed me a lot. Mayber I'll try something handoptimized.. CU later sievers 
20210209, 16:46  #6 
Feb 2021
Salt Lake City, UT
29 Posts 
I excluded giant Mersenne with Mathematica
I managed to exclude a giant Mersennes with Mathematica https://www.mersenneforum.org/showth...ht=Mathematica Pity I later learned they were both known but with Monte Carlo it worked below a Ghz x Minute and they are both above the biggest 2021 Mersenne prime known.
Last fiddled with by mattprim on 20210209 at 16:51 
20210209, 16:52  #7 
"Curtis"
Feb 2005
Riverside, CA
2×3^{2}×5×53 Posts 
"excluded" = trialfactored. Trialfactoring is not at all related to a primality test, and comparing the speed of those two things is akin to someone asking what the 99th power of 99 is, and you answering "Well, I added 99 and 99 really fast!"

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