Remove the prime rib from the refrigerator 3 to 4 hours before cooking so that it can come to room temperature.
When ready to roast, preheat the oven to 500 degrees and move your oven rack to the lower third.
In a bowl, mix the butter and herbs de provence. Cover all surfaces of the meat.
Generously coat the surface of the meat in kosher salt.
Place the roast ribs down into a roasting pan and insert a meat thermometer into the center of thickest section, not touching the rib bones on the bottom.
Wash the potatoes and slice them in to 1/2" slices. Lay them in an even layer around the prime rib to catch drips and prevent the butter from smoking and burning.
Roast your prime rib at 5 minutes per pound. (For an 8 pound roast that's 40 minutes). Then turn the oven off and leave the door closed for two hours.
Monitor the temperature of the meat. If the temperature fails to climb for 15 minutes or begins to fall, turn the oven back on 270 degrees for 5 minutes then turn it off again. Wait 10 minutes for the heat to reach the center of your prime rib. Continue to monitor your meat and make sure the temperature slowly climbs a degree or two every 5 to 10 minutes. If it doesn't turn the oven back on in bursts until you reach your desired degree of doneness. In this case that was 130 degrees.
Remove the prime rib from the oven and leave the meat thermometer inside. Allow the roast to cool to 120 before slicing. That process can take up to an hour depending on how large it is.