This is how I cook prime rib roast. I make it at least a couple of times a month and I like it really rare.
Let the roast sit on the counter for a few hours, to come up to room temp. Preheat the oven to 450 F. Rub the roast all over with a light coating of olive oil. Since you've already marinated it in pesto, skip this step. Sprinkle coarse sea salt over the top. Insert a meat thermometer in the centre of the roast.
Roast for 15-20 minutes at 450 F. Reduce heat to 325 F. Cook to desired internal temp. I usually cook it to about 122-125 F for very rare. For a 3 pound roast, this will take a total of about 45 minutes, but always go by the internal temperature. Actual oven temps can vary wildly.
Remove from oven and let rest for 10-15 minutes, loosely tented with foil. Don't cover it tightly or it will continue to cook in it's own steam. Carve and enjoy!