Bug ? Wilson's Theorem

[Doug Stewart]

Okubok Kenjiro wrote:
> Sir
>
> I know octave is not a tool for number theory, but when I taught
> Wilson's theorem in a high-school I found a bug?
> Wilsons theorem says, for any prime number p, (p-1)!+1 is divisible by p;
> with octave
> rem(prod(1:(p-1)),p) must be zero, my students checked this for all
> primes less than 100. There was an exception for p=29,
> rem(prod(1:28),29), ans=3.514e+13.
> I am a retired mathematician worked in ODE, and am helping highschool
> boys after regular
> classes. To deal with large integers, I teach them to factorize into
> residual classes and their products. I guess octave changes its strategy
> at 29, resulting in this case.
>
> Kenjiro Okubo
> Prof. Emeritus UEC,Tokyo Japan
> _______________________________________________
> Bug-octave mailing list
> Bug-octave at octave.org
> https://www-old.cae.wisc.edu/mailman/listinfo/bug-octave
>
>   
I took a look at your prog. and I don't think Octave will do that question.


try the following change and you will see what I meen.

#wilson's theorem says for any prime p (p-1)!+1 is divisible by p.
format long
plist=[2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97];
for k=1:25
   p=plist(k);
   r=rem(prod(1:(p-1))+3,p);
   printf("%d , %d\n",p,r)
endfor

If you look you will see that I added 3 instead of 1
Now it should not give zero as an answer but it does.
This is because octave cannot produce the big numbers exactly that come 
from the prod() command.

I hope this helps.

Doug Stewart