I've cooked this Prime Rib (PR) twice with a 6.25 and 6.5 pound PRs. This recipe is tops. After reading the comments before cooking both times, the below may be a helpful summation of info and tips.

1. Use a roasting pan that won't shatter at the high temperature; do not cover your meat when cooking. Use the rack in the roasting pan. Add water to the pan up to the rack but not touching the meat. This keeps the meat juicy.
2. Do NOT oil your meat or roasting pan. The high temperature causes the oil to smoke. Do add seasoning to your meat using your favorite seasoning (many suggestions in the comments). It is good to add the seasoning to your thawed PR as you remove it from the refrigerator and set it out 1-3 hours before cooking to come to room temperature. This way, the seasoning sort of "melts" (so delicious when cooked). My rub is garlic powder, sea salt, pepper and dry mustard. If I have powdered Worcestershire seasoning, I add it also.
3. Use the highest temperature your oven will go. 550°F is the best and most accurate with this recipe, otherwise adjust your cooking times on the "per pound" part of the recipe. The formula is 550°F at X-minutes per pound. For my oven, 550°F at 7 minutes per pound is medium rare; 8 minutes per pound is medium with the outside being medium well which is perfect for my husband.
4. After the Per Pound time is over, turn the oven off and do not open the oven door. (Others have had to remove to use their oven for other foods; they wrapped in heavy foil then placed back in the oven, if doing this will have to be figured out for your oven and needs and the comments may be helpful.)
4a. NOTE: If your oven has a fan to cool the temperature after the oven is turned off, you will have to change this recipe formula. From the comments, possibly turn the temp on to around 170°F for the two hours after the 550°F per pound time is over (see comments for more info).
5. You can heat the oven to 400°F at the end of the two hours if you want your meat warmer and it won't effect the perfection of cooking. To do this, at the end of two hours, place your PR back in the oven, turn the oven back on to 400 and when it reaches 400°F, take the meat out. It can be cut then or rest a few minutes.
6. If you want to cook potatoes with your meat, it works beautifully. Due to a comment, I soaked my potatoes for an hour in pure water (not sure if necessary but it worked). I then dried them, rubbed them with a healthy oil and wrapped them very tightly in heavy foil. I placed on the rack with my PR. I used a large white potato and two small sweet potatoes (individually wrapped). Oh boy, they were so-so good! I haven't tried other veggies or other methods.
7. You may have to play with the timing your first time to figure out your oven for your preference, but once you figure it out, oh - this is so easy and delicious.

I loved this recipe. We were also scared but did it on Christmas as well. The recipe says it will work on roast beef as well. Does this include a nice tri tip?

If you cook two 15 lb. roasts, no it does not mean to cook it twice as long..

If your oven only goes to 500°F, leave it in the oven for 3 hours. This is how we have done it for years. Perfect every time!

It's true.. it turns out perfect every time. But my oven only goes to 525°F and I learned the hard way NOT to use a glass dish. It may shatter.

Have done 2 prime rib roasts this way and both were perfect - so I tried a "regular" bottom round roast using the same method. It, too, was perfect. I did ask the butcher to cut my roast leaving some fat on it. It's easy enough to trim after cooking but the fat (in my opinion) adds great flavor and juiciness to the roast. The roasts in the meat case have most all the fat trimmed off.

Hint: Keep your vent on - it can get smokey.

I made this for Christmas dinner and it came out perfect. I let the rib roast sit at room temp (always do) for 1.5 hrs before roasting. I never cover a roast unless it's pot roast and wouldn't think of using a glass pan for roasting. I always use a stainless steel pan with roasting rack. I did not add water and had no problem with smoke although I had just cleaned my oven which is a Frigidaire gas stove about 9 yrs old (good insulation). I roasted a 5.5# rib roast for 28 minutes--it was perfection at rare for me but my husband would say it was raw--he prefers well done. I just put the end piece in a heavy saute pan to finish his off. I can't say that I understand the difference in opinions of this method. If you don't want a rare or medium rare roast, don't bother dry cooking a roast--go for a pot roast or put some steaks on the grill or under the broiler. I also think the oven you have will determine what kind of result you'll get. Some are not insulated enough--others may have too much insulation. One further note, I was very pleased that the juices stayed in the meat and didn't run out at all. As an experiment, I tried roasting potatoes and onions with the meat but I cut them too small (was afraid they wouldn't get done) and they overcooked. Next time, I'll cut them to about 1/2 cup size and they should be fine.

Made in roaster following directions for well done (don't hate) put aujus concentrate with water in bottom than ran tinfoil over the top and punctured holes in tinfoil and put onions on the top of the tin foil than put lid on turned out mantastic

I had a 4.5lb prime rib cooked for 30 mins @ 550°F left it in for 2 hours and it wasn't fully cooked. I don't know what the heck went wrong! The sides were good though, that's what we had to eat because the middle was too pink to consume.

Turned out amazing!!

This is the BEST method to roast a prime rib! I have roasted many over the years, and this was the BEST. I based cooking time on five and a half minutes per pound, and it was right on for medium rare. I added a little water periodically during the 550°F cooking time just to keep it from smoking, but after the oven turned off it took care of itself! This is the only method I will use.

Works every time! Just read about adding some water to the pan to keep the smoke down. Will try that next time. It does tend to smoke the house up without it.

Was so leary of this recipe but went for it anyway for Christmas 2012. This was THEE BEST prime rib I have ever had! I took it out of the frig about an hour before I baked it and seasoned it all over with Montreal Steak Seasoning and put it in the oven as directed. Gulped as I turned off the oven and left it in there for the next 2 hours. Took it out and let it stand on the counter for 20 min. till I sliced it. Perfection! Will always follow this method from now on. No one doubt this recipe. Thank you!!

I was skeptical and quite frankly terrified I would ruin an expensive roast but the result was unbelievable. My daughter and I shared this cooking experience and we were thrilled to serve this perfectly cooked roast to our family. Thank you for saving Christmas dinner. This was our first attempt at cooking a prime rib roast.

This was so amazing. Had a 9.4 lb roast and cooked it 5 mins per lb at 550°F. Set off the fire alarm too but didn't open the door for those two hours and when I did I had two black blobs on top. Thought it was ruined but took that off as it was fat that had bubbled up. When we took the meat from the bone and carved it,it was Fantastic!! It was so helpful to forget it after the first 45 mins and enjoy my company. Would only do it this way from now on. This was my first time cooking a Prime rib. All the comments before really sold me on this idea. Thanks everyone!