Bring prime ribs to cool room temperature (about 1 1/2 hours out of the refrigerator). Make sure you know the weight of the roast.
Preheat oven to 275 degrees.
Season roast extremely well with salt and pepper. Place in roasting pan, fatty side up, and place in oven. Cook until desired degree of doneness is reached (resist the temptation to open the oven door a lot). For rare meat, the roast should take about 20 minutes per pound. When you're within half an hour of your estimated finish time, remove the roast from the oven, and plunge a quick-read thermometer into a fleshy part of the meat near the center (don't do anywhere near a bone). We like to stop cooking the roast in the oven at 115 degrees; this is extremely rare, but the roast will continue to cook as it stands outside the oven (the temperature should go up 5 to 10 degrees). If you remove it at 120 degrees it will be rare, and at 125 degrees it will be medium-rare; we wouldn't recommend going much higher than that.
Place the roast on a cutting board, uncovered, and let it rest for 15 minutes.
When ready to serve, simply cut the meat away from the bone in one enormous chunk. Then, cut the "filet" of meat into slices and serve immediately. Cut through the bones (you'll have 5), and serve them separately.
(Recipe courtesy of David Rosengarten, Taste cookbook, Random House, 1998)