Gaussian Mersenne Primes of the form $x^2+d{y}^2$

Sushma Palimar, Ambedkar Dukkipati

In this paper we study Gaussian ring $\mathbb{Z}[i]$ with a focus on representing Gaussian Mersenne primes $G_p$ in the form $x^2+7y^2$. Interestingly when such a form exists, one can obse…