Standing Rib Roast Cooking Times

Over the past 10 years I have kept track of how long I have cooked various sized Standing Rib Roasts, aka, Prime Rib. The reason it is called a "Standing Rib Roast" is that "Prime" is a grade reserved mostly for restaurants. You are likely getting Choice or Select grade meat. Any other grade goes down in quality quickly after that. This year we have a 12 1/2 lb Angus Standing Rib Roast!
When choosing a rib roast, think also of how you are going to carve and serve it. If you carve the ribs apart after roasting, the meat is a good 1 1/2" thick and takes up the entire plate. It also doesn't go very far and you'll need doggie bags. I always order it off the bone but have it retied. The bone helps flavor the meat as well as reduce cooking time plus keeps it upright in the oven. Once the meat rests, untie it and carve your desired thickness, ideally 3/4" thick. Keep the bone for a later meal as there is a lot of meat on it and it is really good!
The smallest roast I get regardless of whether there are just 2 of us is 3 bones. I think this ends up about a 3 1/2 - 4 lb roast. If it doesn't have 3 bones it will fall over as it shinks in the cooking process and it will cook unevenly.
Next, you have to have a roasting pan long enough to fit your rib roast. You can buy those at a reasonable price now. I would not use glass for a rib roast but rather a roasting pan. Once the meat is done, you will need a carving board large enough. One with a well to collect juices is best. You will also need a very sharp carving knife. When setting the table don't forget sharp knives. Remind your guests to kindly not cut into you silver plate or sterling silver forks when cutting. For this occasion, I would cut children's meat on the carving board and serve theirs ready to eat.

Preheat oven to 350. Place oven shelf 1 level below center making sure the roast will fit in the space without touching the heating element. If it looks too close, lower the shelf one more time.
Place roast in the pan. S&P the outside of the meat. If you like herbs, thyme is a good choice. Quarter an onion creating fairly large wedges, cutting from north to south poles. To prevent burning, do not pull apart every layer. Arrange in bottom of the pan. 

Place in the oven WITHOUT covering. If you cover it you are steaming the meat.

4.36 lbs 1 hour 25 minutes
4.6 lbs 1 hour 25 minutes
5 1/2 Lbs 1 hour 30 minutes
6 1/2 lbs 1 hour 45 minutes

7.75 lbs 1 hour 55 minutes
10.4 lbs 2 hours 20 minutes
17 3/4 lbs 2 hours 20 minutes

You can see that once the meat is longer than it is wide it doesn't cook any longer. It took me a few thoughtful hours to figure this out. Once I came to that conclusion with my $100+ 17 lb rib roast and finally called Houston's Restaurant to make certain of my thought process. They were nice enough to confirm this and the roast was prefect!