Place the standing rib roast in a large roasting bag or deep container.
Add the red wine and crushed garlic.
Cover and refrigerate overnight.
Remove the roast from the refrigerator 2–3 hours before cooking so it comes closer to room temperature.
Preheat oven to 500°F.
Remove roast from marinade and discard marinade.
Pat the roast completely dry with paper towels.
Season generously with kosher salt and black pepper on all sides.
Place the roast bone-side down in a roasting pan fitted with a rack.
Roast for 15 minutes to develop a crust.
Reduce oven temperature to 325°F.
Insert a probe thermometer into the center of the roast from the side.
Continue roasting until internal temperature reaches:
120–125°F for rare
130–135°F for medium rare
140–145°F for medium
Remove roast from oven when it is about 10 degrees below desired final temperature.
Tent loosely with foil.
Rest for 20–30 minutes before slicing.
Slice and serve immediately.
Notes
Prime rib continues cooking while resting (carryover cooking), so remove it from the oven about 10°F before your target temperature.
Medium rare is the most popular doneness for prime rib.
Cooking time varies depending on roast thickness, oven accuracy, and starting temperature, so always use a thermometer instead of relying only on time.