Here's one way to cook a Prime Rib Roast. While clearly not the only way, this seems to work pretty well in a "home" context; no special ovens needed, and cooked in reasonable time with reasonable food safety...

This particular prime rib was new-years-day dinner... yum.

(That's me cooking. The purple one took most of the pictures.)

Step 1: Ingredients and Equipment

This particular recipe is for "rock salt roasted prime rib of beef", or something like that. The roast is buried in rock salt, which keeps the outside from getting burnt and absorbs fat/etc while the roast cooks in a rather hot oven. (In general, the difficulty with large roasts like prime rib is getting the inside and the outside cooked to edible doneness levels at the same time.)

Prime rib of beef. These show up in normal markets around major holidays, and are probably in your better butchers and wholesale clubs and such all the time, or perhaps can be ordered. These days a prime rib roast is available either boneless or with the ribs still attached; cost per pound is somewhat less for the bony version, but cost per roast is about the same (based on my looking at CostCo.) I usually get boneless roasts for convenience of carving and serving; other people believe that the bones add flavor. I don't have any particular hints on how to tell a good roast from a bad roast; you pretty much have to trust your butcher. A whole prime rib will weigh more than 15 pounds and cost over $100. But it will feed 20+ people, so that's not really as bad as it sounds. Hereafter the roast shall be referred to as "the Beast."
Large Pan. This should be large and deep enough to contain the whole Beast in all three dimensions, plus enough room for the salt.
Rock salt. Enough to bury the whole Beast. About 10 to 15 pounds. You probably don't want to use rock salt that is targeted toward melting ice on driveways; the stuff I use claims to be for making homemade ice-cream.
Other seasonings to taste. Or not (see later.)
Meat thermometer. There are two common varieties of meat thermometer. One is designed to sit in your roast in the oven while it cooks. The other is an "instant read", that you're supposed to stick in to check the temp, but NOT leave in the oven... The former is preferred, so you can keep a continuous eye on how the cooking is proceeding.

Step 2: Open, Trim, and Season the Beast.

Take the Beast out of its plastic, wipe off the excess blood/juice with some paper toweling, and season on the outside with whatever spices you want. Garlic and Pepper are popular; However, this is a THICK piece of meat, and not a lot of the flavoring is going to penetrate to the best areas for eating anyway (especially if you have bones.) It is probably better to provide an assortment of seasonings for the diners to add to their slices just before eating. (this particular Beast was not seasoned at all.)

You may have to cut the beast down to fit in your pan (and/or oven.)

Step 3: Bury the Beast in Rock Salt.

Put a layer of rock salt (about one inch deep) in the bottom of your pan, put the meat on top of that, and add more rock salt to essentially bury it. You can add foil over the meatier sections if you're concerned about the amount of salt that will end up in the roast, but like the spices, not that much will penetrate very far into the meat anyway; mostly the salt sorta seals in moisture and allows drainage space for fat. I generally use a layer of foil if I have a boneless roast with bare meat exposed.

Keep in mind that you now have 15 pounds of meat and 10+ pounds of rock salt in this pan, so it's going to be pretty heavy. Practice using your oven mitts; when it's hot is not the time to discover that you can't get a good grip on it.

In retrospect, it woulld have been a good idea to insert the thermometer into the thickest portion of the meat before it was entirely covered with salt. But I forgot.

Step 4: Cook at High Heat Until (almost) Done.

Throw it into a preheated oven at about 425F. It will start to smell ... tempting ... in about 30 minutes, but you're probably looking at about two hours till you've hit "rare." (so say the jpg timestamps!)

You want to cook until the thermometer is ALMOST at the desired degree of done-ness.
Done-ness is a matter of personal preference, but remember that the ends will be more well done than the middle, and that you can always cook an underdone slice a bit extra in a microwave, but you can never un-cook an overcooked piece. Also, you'll have to get used to your thermometer and the lies it tells.

All that said, I think this is the first year that the Beast came out as rare as I wanted it to. My first attempt several years ago was (by my standards) pretty drastically overcooked, but it didn't taste as bad as I would have thought. This cut of meat, and this method of cooking, seems to leave quite a lot of flavor over a wide range of mistakes.

Step 5: Remove From Oven BEFORE Fully Cooked...

You beef is surrounded by hot salt, so it will continue cooking for a bit after it is taken out of the oven. This means you want to take it out somewhat before the thermometer registers the dessired temperature.

Here you see it coming out of the oven with the needle just below the 130F "rare" mark. Keep an eye on that dial through the next couple of steps to see how it continues to creep upward.

As you can see in the photo, the salt at the ends of the Beast will have been partially melted away by the juices seeping out; if you're using an instant-read thermometer this can be your cue to start checking the temperature fairly frequently.

It seems to be the nature of cooking that the temperature moves pretty quickly once it starts moving; so keep an eye on it!

Step 6: Allow to Cool (and Cook Outside the Oven) Somewhat.

400F salt crystals are not something you want to drop into your slippers! Let the Beast sit for 10 or 15 minutes so they'll cool down slightly. It will continue to cook a bit during this time... Collect your excavating, lifting, and carving implements.

Step 7: Excavate the Beast.

Carefully remove the salt from top and sides of the beef, putting it somewhere where it won't do too much damage. I use a double paper bag inside a heavy-duty (trash compactor) plastic bag. The paper is pretty heat resistant, and the plastic won't leak grease/fat. Careful; it's still hot. You want to remove enough salt from the top and sides that you can lift out the beast without scattering too much hot salt all over everywhere. (that's almost all of the salt from the tops and sides.)

Step 8: Remove Beast to Carving Platter.

Using several strong, large forks (like barbecue tools), carefully lift the beef to another platter for carving. Don't scatter hot greasy salt everywhere!

Step 9: Slice and Serve

Slice as appropriate for your consumers. All at once, or slice-at-a-time. Thick or thin. Rare pieces from the middle of the thicker areas, more well done from the ends...

If you have bones, I think it's traditional to slice "he-man" cuts mid-way between bones, and "petite" cuts right along the bone edges with an additional slice from between bones.

A disadvantage of this method of cooking is that you won't have useful "pan drippings" from the cooking pan; they'll be hopelessly salty. However, you should wind up with plenty of juices from the carving process.

Serve with your favorite seasonings: horseradish, pepper, salt, seasoned salt, etc.

YUM

Step 10: Cleanup.

Salt saturated with Beef Fat is not something you want to put down your kitchen sink. The salt that was under the beast will now be a solid mass of salt/fat composite material capable of giving concrete a run for it's money in the strength department. When it's time to clean up, put the pan back in a low oven (250 F) to heat and soften the fat and partially dissolve the salt in juices. Then break up the mass with a suitable tool and dump it in your triple-layer salt waste disposal bag.