201401.6656v1 Gaussian Mersenne Primes of the form x^2+dy^2

In this paper we study Gaussian Mersenne primes in the form x^2 +dy^2 , for some square-free integer d>0 . Gaussian Mersenne primes are given by GMp=2^p −(2/p)2^((p+1)/2)+1 , where (2/p) is the Legendre symbol 2modp . We show that, these primes can be represented in the form x 2 +dy 2 , for d≡1,2,3,4,5,6,7mod8 . Computationa..