Don’t add water or any liquid to the pan.
Preheat your oven to 450°F and then place the roast, uncovered, in the oven and cook for just 15 minutes. This gets the outside cooking quickly so it forms a nice crust while baking.
Lower the temperature to 325°F. Cook for approximately 60 to 90 minutes more or until a meat thermometer inserted in the middle of the roast reaches 135°F. Keep in mind that the internal temperature will increase 10°F to 145°F (medium-rare) once the roast is removed from the oven and stands for 10-15 minutes.
Letting the roast rest after cooking and before slicing allows it to retain its juices. While some people like to tent the roast loosely with aluminum foil as it rests, I prefer not to because the internal temperature might rise too much and you also might lose the crispy crust.
I think a prime rib is best served medium rare to medium. For me, anything over 160°F (medium) after standing is too dry and overcooked, but doneness is a personal preference.