Mersenne: Fast check for common factor?

[Alexander Kruppa]

Hi,

I�m thinking about something the would probably be called a stage 2 for
my P-1 factorer, i.e. the 3^(E*(p+x)) = 3^(E*p) * 3^(E+x) with x
difference between subsequent primes.
But I need to check for a factor after every of these steps, and a
full-blown GCD would be far too slow. Is there another trick to find out
whether two numbers have a common factor (without neccessarily finding
the factor itself) ?

Ciao,
  Alex.