A347300 Under Hypothesis(H) (a version of the Generalized Riemann Hypothesis) the only principal real quadratic fields with discriminant d = r^2 + 1 == 1 (mod 4) are the fields Q(sqrt(t)) where t is one of the six numbers listed here.
5, 17, 37, 101, 197, 677
Offset: 1
References
- Gilles Lachaud, On real quadratic fields, Bull. Amer. Math. Soc., 17:2 (1987), 307-311. See Theorem 3.2.