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Place prime rib roast on a plate and bring to room temperature, 2 to 4 hours.
Preheat the oven to 500 degrees F (260 degrees C).
Combine butter, pepper, and herbes de Provence in a bowl; mix until well blended. Spread butter mixture evenly over entire roast. Season roast generously with kosher salt.
Roast the 4-pound roast in the preheated oven for 20 minutes. (If your roast is larger or smaller than 4 pounds, multiply the exact weight times 5 minutes.)
Turn the oven off and, leaving the roast in the oven with the door closed, let the roast sit in the oven for 2 hours.
Remove roast from the oven, slice, and serve.