MERSENNE PRIMES

A positive integer n is called a perfect number if it is equal to the sum of all of its positive divisors, excluding n itself.For example, 6 is the first perfect number because 6=1+2+3. The next is 28=1+2+4+7+14. The next two are 496 and 8128.
Theorem One: k is an even perfect number if and only if it has the form 2n-1(2n-1) and 2n-1 is prime
Theorem Two...If 2n-1 is prime, then so is n.
Theorem Three: Let p and q be primes. If q divides Mp = 2p-1, then
q = +/-1 (mod 8) and q = 2kp + 1
for some integer k.
THEOREM Four.. Let p = 3 (mod 4) be prime. 2p+1 is also prime if and only if 2p+1 divides Mp.