Bug ? Wilson's Theorem

[Okubok Kenjiro]

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