1. Prepare grill for indirect grilling with a large dripping pan under where the roast will be. Aim for a grill temperature around 375*F. Periodically add water to the pan to keep the drippings from burning away if you want to make gravy. Make sure you know the weight of your prime rib. Plan on grilling indirectly for 12 to 14 minutes per pound. If you are using a smaller roast, adjust the ingredients and cooking times accordingly.
2. With a sharp paring knife make a series of 1/2 inch deep holes every 2 inches all over the roast. Insert the garlic slivers in every other hole and a leaf from the rosemary in the rest. Combine black pepper, dried rosemary, salt and paprika and rub over the surface of the meat. When the grill is ready, place the roast on the well oiled grate directly over the dripping pan. Cook for about 12 to 14 minutes per pound. An 18 pound roast will take about 3 1/2 to 4 hours. It is very important to use an accurate meat thermometer to check for doneness. You do not want to over cook this roast.
3. When the meat reaches an internal temperature of 115 to 125*F. remove it from the grill. Place it on a platter and cover loosely with foil. The meat will continue cooking and the internal temperature will continue to rise. Let rest for at least 15 minutes, but no more than 30. If you want the roast rare to medium rare, remove from the grill when the temperature is 115*F. and let it rest for 15 minutes. If you want it more well done, remove from the grill at 125*F. and let it rest for 30 minutes.
My Note: I made a 7 rib, 12.21 lb prime rib with this receipe for Easter and to day that it was wonderful is a understatement. I did not use the dried rosemary on the rub since I but extra garlic and fresh rosemary in the slits and I am glad that I used the fresh instead. everyone raved aboutit and this 24 people. I could not make copies fast enough for all the people who wanted the recipe. The best thing is once it was on the grill, I didn't need to think about it at all. UPDATE: I used fresh rosemary and garlic as suggested. Only change - I used cayenne ILO of paprika in my rub. Cooked faster than recipe said, but turned out medium to medium rare with internal temp of 140 when I pulled it off the grill. I used a Brinkman four flame gas grill and tried to keep the temp at 325*F. My roast was 14.5 pounds and total cooking time was just under 3 hours. Everyone love it - so that is my measure.