There are different ways to cook a prime rib. First the easiest:
Method #1–Take your Prime Rib out of the Fridge a couple of hours before cooking to let it warm up. Before putting it into the oven very liberally treat the entire roast with sea salt and pepper. Preheat the oven to 500 degrees Place the Prime Rib in a cooking pan. Put the Prime Rib Roast in the oven at 500 degrees for 5 minutes a pound for medium rare, 6 minutes a pound for medium-to medium well. (pink, not bloody) Turn the oven off after the minutes a pound is reached. Do not open the oven for 2 hours. At the end of two hours, remove the Prime Rib Roast and cover with foil loosely and let it rest for 20 minutes. Slice and serve. If you cut the roast before letting it rest, the juice will drain and the meat will not be moist.
Method #2— Prepare the prime rib as before for cooking. Preheat the oven to 400 degrees. Cook the roast for 30 minutes then reduce the heat to 325 degrees and cook for 11 minutes per pound. The roast should be at 12- to 125 degrees for medium rare. Add 10 more degrees for medium. Tent with foil and let it rest for 20 minutes before serving.
There are other methods of cooking ribs. All have the same goal–searing the outside for the flavor and cooking till about 120 degrees for medium rare and about 130 for medium.