The torsion order elliptic curves over $\mathbb{Q}$ with prime conductor have been well studied. In particular, we know that for an elliptic curve $E/\mathbb{Q}$ with conductor $p$ a prime, if $p > 37$, then $E$ has either no torsion, or is a Neumann-Setzer curve and has torsion order 2. In this talk we examine similar behavior for elliptic curves of prime conductor defined over totally real number fields.