The following theorem might help :

Fermat, a French mathematician, once proved that : " If p is a prime number whilst GCD(p,a)==1 then a^p-1 is congruous to 1 modulo p." But actually this theorem isn't enough, it helps you prove a number is not prime, not the other way round...

Lucas, another French dude, came up with yet another theorem which looks for Mersenne's prime numbers :
Given p an odd number, the number M=2^p-1 is prime if and only if 2^p-1 divides S(p-1) where S(n+1)=S(n)² - 2, and S(1) = 4.

Further down the road, Indian scientists came up with a very interesting paper you may want to check out : they probably have an answer to your problem : <a href=http://www.cse.iitk.ac.in/news/primality.pdf>primality.pdf</a>...

Hopefully, I've been of some help - maths are really interesting and I always enjoy digging into them...