When cooking prime rib at 250 degrees in the oven you should preheat the oven to 250 degrees while preparing your prime rib.
Then place the prime rib into the preheated oven and let it cook for around 3 to 4 hours depending on how well done you want the prime rib.
For me I cook the prime rib in the oven for 3 and 1/2 hours which is good enough for me.
If you have a meat thermometer you can test the internal temperature of the prime rib which should be 120 degrees F when fully done.
But as long as you cook the prime rib for at least 3 hours or 3 and 1/2 hours the prime rib should be fully cooked and ready to eat once it cools down.