Preheat oven to 450°F.
Pat the prime rib dry with paper towels.
Season the roast with 1 teaspoon salt and ½ teaspoon black pepper.
Place the roast, fat side up, on a roasting rack set inside a roasting pan.
In a food processor, pulse the cranberries until finely chopped.
Add horseradish, Dijon mustard, breadcrumbs, garlic, olive oil, 1 teaspoon salt, ½ teaspoon black pepper, rosemary, and thyme.
Pulse until the mixture is combined and crumbly.
Spread the cranberry mixture evenly over the top and sides of the roast, pressing gently so it adheres.
Roast at 450°F for 20 minutes.
Reduce oven temperature to 325°F.
Continue roasting until the internal temperature reaches 125°F for medium rare, about 15–20 minutes per pound.
Remove the roast from the oven and tent loosely with foil.
Rest for 20 minutes before slicing.