Mersenne: (2^p-1)/p == 0 (mod 3) ?

[Alexander Kruppa]

Hello all,

a simple Number Theory question. Is always

(2^p-1) / p ,odd prime p, divisible by 3 ?

Then 2^p == 1 (mod 3p) would also hold, can this be used to improve the
efficiency of a Rabin-Miller probable prime test?

Ciao,
  Alex.
_________________________________________________________________
Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm
Mersenne Prime FAQ      -- http://www.tasam.com/~lrwiman/FAQ-mers