Primes of the form $x^2+d{y}^2$ with $x\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}N)$ or $y\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}N)$

In this paper we charatcterize primes of the form $x^2+d{y}^2$ with $x\equiv 0\pmod{N}$or$y\equiv 0\pmod{N}$forpositiveinteger$N$and$d$with$d$ being square free.