K. Raja Rama Gandhi, Primes of the form x2 + ny2, Volume 3, The Bulletin of Society for Mathematical Services and Standards (Volume 3) https://www.scipress.com/BSMaSS.3.67 Abstract: We know that, Fermat Showed a prime can be expressed as a sum of two squares if and only if it is a multiple of four plus one and its decomposition is unique. This paper will discuss the similar writings of primes as a sum of squares and multiple of another square. Keywords: Fermat Sum of Two Squares, Lattice Points, Mersenne Prime, Quadratic Reciprocity, Ring of Gaussian Integers