Form of Fermat Primes
Fermat number is of form 2**(2**n) + 1, if prime is said to be Fermat Prime
LEMMA 1
If 2**m + 1 prime, then m=2**n [n>0]
Proof:
Suppose m has odd divisor 2k+1, then
2**m + 1 = 2**((2k+1)r) + 1
=(2**r)**(2k+1) + 1
=(2**r + 1)(2**(2kr) - 2**((2k-1)r) + … + 2**(2r) - 2**r + 1)
not prime