A three rib is WAY too much. We got a 3-rib for Thanksgiving for 3 of us, and wound up freezing some of the leftovers. We only ate maybe 2/5th of it. A 2-rib roast is better.
Use the method we've been discussing, and it will be perfect.

Here is a link that might be useful: perfect prime rib

As long as the internal temperature is not too high (I think of medium rare as 120F or so), it won't dry out.

You can experiment with various interesting approaches. For simplicity's sake, and assuming you're not fanatical about exactly how many millimeters of gray meat you'll tolerate, I would simply do this:

- Take roast from refrigerator. Rub meat all over with salt. Let it sit on the counter until it gets to room temperature, 60-70F, a couple hours.
- Pre-heat oven to 200F, place roast in oven with probe thermometer inserted in the center. Remove when center's temp is 90F, and wait 1/2 hour for temp to even out. Exterior of roast is hottest e.g. 150F, center is coldest e.g. 90F, as temp evens out the center's temp will rise. If center's temp stabilizes below 110F, put roast back in oven for a bit and repeat until center stabilizes around 110F, or close enough.
- Heat empty cast iron pan over high burner for 5 minutes. Squirt some oil into the pan, heat the oil until it is smoking and spitting. Place roast in pan to sear, check it every minute to see if it is crusty and brown enough for you. Don't exceed 3 minutes searing. Because the roast is already close to 110F throughout, you shouldn't have to sear for too long and won't create too much of an overcooked gray band. If you keep the probe in the meat while searing, you can make sure the center temp doesn't get above 115 F. No need to "rest" after searing, you can wait a bit to let center temp rise to the desired 120 F, but if the temp looks like it is going to overshoot, you can slice it pronto.
- The pan has to be really! rocket! hot!, otherwise you will turn the whole roast overcooked and gray before you achieve browning. If you prefer, you can instead put the broiler on high, and sear by holding the roast right up in the flames for a minute.

The reason I'm suggesting this process is that with a small roast, it makes sense to take special care to minimize the gray band, as it could otherwise be a large percent of the meat. Just putting a 2-3 lb roast into a 400F oven runs the risk of overcooking the meat before you can get a nice crusty sear.

Bumping this because lots of people have plans for prime rib this week.

Bump

We'll be putting ours on the BBQ. Easiest way to get a good result, I think. But, We cook a single rib at a time.