For ease in carving, ask your butcher to cut the meat off of the ribs and chine (backbone) and tie it back on.
The day before you plan to roast your prime rib, season it liberally on all sides with salt and pepper. Place the roast on a heavy baking sheet with the fat cap side up and refrigerate, uncovered, overnight (or up to 24 hours).
Remove the prime rib from the refrigerator and let stand at room temperature for 2 hours before roasting.
Preheat oven to 250°F with the rack in the lower third of the oven. Place prime rib on a v-rack in a roasting pan with the fat-cap side up.
Roast until an instant-read thermometer inserted into the thickest part of the meat (away from the bone) reads 120-125°F for rare, 128-130°F for medium-rare, or 132-135°F for medium and medium-well. This will take 3-4 hours.
Remove the prime rib from the oven, tent with foil, and let rest for 30 minutes.
Increase oven temperature to 500°F. Uncover the roast and sear it in the oven for 5-10 minutes, until the exterior is brown with a crisp crust.
*The prime rib photographed in this post was a 4-rib roast weighing 11 pounds. It was cooked to an internal temperature of 120°F in about 3 hours and 20 minutes.
Especially when slow roasting at a low temperature, it's important to confirm that your oven is running true to temperature with a reliable oven thermometer before you get started. Read how to test it with this article from Fine Cooking.