How should I cook a 3.5 pound rib roast - prime rib?

I did this at Christmas. Multiply the weight of the roast by 5 (with your roast the number would be 17.5) Bring your roast to room temperature (two or three hours) and coat with mustard, garlic and thyme (or your favorite rub). Preheat the oven to 500°F. Put the roast in the oven and turn the oven off after 17.5 minutes. Don't touch or open the oven for two hours.You will have a perfectly medium rare roast.

After warming and searing the meat, 15-20 minutes per lb at 325 F, or until the internal temp reaches 125 F. Remove from the oven and cover with foil, allowing the roast to rest for 20 minutes before serving.

Remove roast from fridge 2 hours before cooking. Preheat oven to 250. Rub cuts ends and fat side with oil and then generously salt and pepper it. Heat ovenproof saute pan over medium heat until hot. Brown meat on all three sides, perhaps 4 minutes each. Place bone-side down and place in oven. Cook til 120-130 for rare to med. rare. This may only take 45 minutes so check after 30. I've used this technique since 2002 with always great results.

Well, you want it to sit out for 30 minutes to warm up a bit from the refrigerator .. so it will cook more evenly.

And you want to start off with a high temp in the oven to sear the outside

Roughly, depending on how rare/welldone you like it about 20-30 minutes per pound at 350 or 375.

Just google it.