The 4 Fermat prime can be calculated as:
F0 = 2^(2^0) + 1 = 2+1 = 3
F1 = 2^(2^1) = 4+1 = 5
F2 = 2^(2^2) + 1 = 16+1 = 17
F3 = 2^(2^3) + 1 = 256+1 = 257
Hence the first four Fernat Primes are 3 5 17 257.
A Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2^n − 1 for some integer n.
Hence first few Mersenne prime numbers are:
3, 7, 31, 127, 8191 corresponding to indices n=2, 3, 5, 7, 13