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Preheat the oven to 500°F (260°C).
Mix together the butter, garlic, herbs, salt, and pepper in a medium bowl until evenly combined.
Rub the herb butter all over the rib roast, then place on a roasting tray with a rack.
Bake for 5 minutes per pound (10 minutes per kilo) of meat, 25 minutes for a 5-pound (2.2 kg) roast.
Turn off the heat and let the rib roast sit in the oven for 2 hours, making sure you do not open the oven door or else the residual heat will escape.
Once the 2 hours are up, remove the roast from the pan and pour the pan drippings into a saucepan over medium heat.
Add the flour, whisking until there are no lumps, then add the beef stock, stirring and bringing the sauce to a boil.
Remove from heat and strain the sauce into a gravy dish.
Carve the prime rib into ¾-inch (20-mm)-thick slices.
Serve with the mashed potatoes, green beans, and the pan sauce.