Chef John's Perfect Prime Rib - Prime Rib 2

This recipe was discovered by sister Kathy.  We have used it for the past 2 Christmas dinners which resulted in perfect prime rib.  *note to let roast sit at room temperature for 4 hours prior to cooking - this is a key step to this recipe.  Use the formula listed below to calculate cooking time for different size roasts.
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• 4 pounds prime rib roast
• 1/4 cup butter, softened
• 1 tablespoon freshly ground black pepper
• 1 teaspoon herbes de Provence
• Kosher salt

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Directions

1.  Place rib roast on a plate and bring to room temperature, about 4 hours.
   
2. Preheat oven to 500 degrees
3. Combine butter, pepper, and herbes de Provence in bowl; mix until well blended.  Spread butter mixture evenly over entire roast.  Season roast generously with kosher salt.
4. Roast the 4-pound prime rib (see comments below for larger and smaller roast) in the preheated oven for 20 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.

Cooks Note:  

• "This is a specific formula for achieving a perfectly pink prime rib cooked somewhere a shade under medium rare. To use this method you must have a full-sized, modern oven with a digital temperature setting that indicates when it is preheated. Older ovens with manual controls can vary greatly, and the doors may not have the proper insulation."
  
• Your cooking times will vary depending on the size of your prime rib roast. To calculate your cooking time, multiply the exact weight of the roast by 5. Round the resulting number to the nearest whole number. The rib is cooked at 500 degrees F for exactly that many minutes. For example, for a 6 pound roast: 6x5=30, so cooking time is 30 minutes. Turn the oven off and wait 2 hours before opening the oven door. Remove the prime rib and slice into the most perfectly medium-rare meat you've ever seen.