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See [Cox, Primes of the form $x^2 + ny^2$], p. 110, Theorem 5.26. There are infinitely many such primes since infinitely many primes split completely in the Hilbert class field, which follows from Chebotarev's density theorem, but there is also a completely elementary argument (analogously to Euclid's proof that there are infinitely many primes).

See [Cox, Primes of the form $x^2 + ny^2$], p. 110, Theorem 5.26. There are infinitely many such primes since infinitely many primes split completely in the Hilbert class field, which follows from Chebotarev's density theorem, but there is also a completely elementary argument (analogous to Euclid's proof that there are infinitely many primes).

See [Cox, Primes of the form $x^2 + ny^2$], p. 110, Theorem 5.26. There are infinitely many such primes since infinitely many primes split completely in the Hilbert class field, which follows from Chebotarev's density theorem, but there is also a completely elementary argument.

See [Cox, Primes of the form $x^2 + ny^2$], p. 110, Theorem 5.26. There are infinitely many such primes since infinitely many primes split completely in the Hilbert class field, which follows from Chebotarev's density theorem, but there is also a completely elementary argument (analogously to Euclid's proof that there are infinitely many primes).

See [Cox, Primes of the form $x^2 + ny^2$], p. 110, Theorem 5.26. There are infinitely many such primes since infinitely many primes split completely in the Hilbert class field, which follows from Chebotarev's density theorem, but there is also a completely elementary argument.

See also [Cox, Primes of the form $x^2 + ny^2$], p. 186, Theorem 9.8(ii).

See [Cox, Primes of the form $x^2 + ny^2$], p. 110, Theorem 5.26. There are infinitely many such primes since infinitely many primes split completely in the Hilbert class field, which follows from Chebotarev's density theorem, but there is also a completely elementary argument.