Primes of the form x 2 + d y 2 with x ≡ 0(mod N) or y ≡ 0(mod N)

Berrizbeitia P and Iskra B, Gaussian–Mersenne and Eisenstein–Mersenne primes , Math. Comput. 79 (271) (2010) 1779–1791 Cohen H and Stevenhagen P, Computational class field theory, in: Algorithmic number theory (eds) J Buhler and P Stevenhagen (2008) (MSRI Publications) vol. 44 Cohen H, A course in computational algebraic number theory (1996) (Berlin: Springer-Verlag) Cohen H, Advanced topics in computational number theory (2000) (New York: Springer-Verlag) Cohen H and Stevenhagen P, Arithmetic of number rings, in: Algorithmic number theory (eds.) J Buhler and P Stevenhagen (2008) (MSRI Publications) vol. 44 Cox D A, Primes of the form x 2 + n y 2 Fermat, class field theory and complex multiplication (1989) (John Wiley & Sons) Jansen B, Mersenne primes and class field theory, Ph.D. thesis (2012) (Netherlands: Universiteit Leiden) Jansen B, Mersenne primes of the form x 2 + d y 2, Master’s thesis (2002) (Netherlands: Universiteit Leiden) Lang S, Algebraic number theory (1994) (New York: Springer-Verlag) Lemmermeyer F, Construction of Hilbert 2-class fields, citeseer Lenstra H W and Stevenhagen P, Mersenne primes and Artin reciprocity, Nieuw Archief voor Wiskunde 5 (1) (2000) 44–54 Palimar S and Shankar B R, Mersenne primes in real quadratic fields, J. Integer Sequences 15 (5) (2012) 1–12 Vaugham T P, The construction of unramified cyclic quartic extension of \(\mathbb {Q}(\sqrt {m})\) , Math. Comput. 45 (171) (1985) 233–242