Preheat the oven to 450 degrees F.
Season the prime rib roast liberally with salt and pepper, then place it on a rack set inside a roasting pan and roast for 30 minutes. Turn down the oven temperature to 350 degrees F and roast until an instant-read thermometer inserted into the thickest part of the roast reads 130 degrees F for medium-rare, about 1 1/2 hours. Transfer the meat to a platter and tent with foil to keep warm.
Place the roasting pan on top of the stove. Turn 2 burners to high heat, add the butter to the pan and use a wooden spoon to stir and scrape the bottom of the pan. Add the beef stock and red wine and cook until the liquid is reduced by half, about 20 minutes. Whisk in the rosemary and season with salt and pepper.
Slice the meat between the bones into individual steaks and serve each with the red wine au jus.