Combine butter, ginger, orange zest, garlic, salt, pepper, soy sauce, brown sugar, and rosemary.
Spread butter rub over the prime rib and place on a roasting rack in a roasting pan (see note).
Add water to the bottom of the roasting pan.
Roast at 450ºF for 20 minutes.
Reduce the oven temperature to 325º F and continue to roast until medium-rare (130-135ºF), about 1.5 hours. Check the water in the roasting pan and the temperature of the prime rib roast after about 1-hour, adding more water if necessary.
Remove the prime rib roast from the oven and let it rest for 15-20 minutes before slicing and serving.
Cut and remove the strings and slice the prime rib, or remove the bottom bones (they will just slide off) if you want to serve thinner slices.
You can use 3 balls of foil to elevate the roast in the pan if you don't have a rack.