I cook prime ribs often, and this is the process I follow, almost guaranteed not to fail:
Let the roast (mine is usually between 7 - 8 pounds) sit out out on the counter, in its wrappings, to come to room temperature for at least one hour, depending upon the size. Longer if it's a larger roast.
Pre-heat the oven to 450.
Season the roast if you like, but not with salt because salt draws out the moisture.
Place the roast, fat side up, on an open roasting pan with low sides.
Sear for 10 minutes, up to 15 minutes, if it's a larger roast than 7 - 8 pounds.
Reduce heat to 325.
Leave the roast uncovered, basting the cut sides, only, every half-hour with pan drippings. The top is already being basted with the fat from the roast.
The cooking time will vary depending upon your oven, which is why you need a good digital meat thermometer. Cook to 120-125 F. for rare and 125-130 for medium rare.
Remove from oven, tent with foil and let it rest for 15-20 minutes. The internal temperature will rise by at least another 5 degrees.
Don't forget the au jus, gravy, if you prefer, and yorkshire pudding.