To prove 2^p-1 is prime at first it looks like we have to check every smaller number to see whether it divides this number. But the combined efforts of Lucas and later Lehmer has shown that 2^p-1 is prime provided it divides a number L(p) called the Lucas-Lehmer number. How are L(p) defined?L(3)=4 and L(n)=L(n-1)²-2.

Your computer just needs to generate this list of numbers and then check is the pth Mersenne number divides the pth Lucas-Lehmer number.