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In this paper we charatcterize primes of the form $x^2+dy^2$ with $x\equiv0\pmod{N}$ or $y\equiv 0\pmod{N}$ for positive integer $N$ and $d$ with $d$being square free.

Primes of the form $x^2+dy^2$ with $x\equiv 0\pmod{N}$ or $y\equiv 0\pmod{N}$