So the problem has to deal with Mersenne numbers 2^p-1 where p is a odd prime, and Mp may or may not end up being prime. The theorem given is: If p is an odd prime, but Mp=2^p-1 is not a Mersenne prime, then every divisor of the Mersenne number 2^p-1 is of the form 2*c*p+1 where c is a nonnegative integer. Assuming this theorem is true, I need to somehow use it to determine whether M(13)=2^11-1=2047 and M(23)=2^23-1=8388607 are prime. I know it's supposed to start with something like "If 2047 is not prime, then we know it must have prime factor <=sqrt(2047) which is about 45.24...but I am unsure of where to go from there. Help would be awesome! Thanks!