Today I am cooking a 4.24 lb Prime Rib from compared with 3.23 lb for my previous one. I wonder if I can predict how long it will take other things being equal. The first result on Google for "time for roasting prime rib by weight" returns an article that says 15 min / pound which suggests that the time scales proportional to weight.

$$rate = \frac{time_1}{weight_1}$$
$$rate = \frac{5 \operatorname{hrs}}{3.23 \operatorname{lb}} = 1.55 \operatorname{hrs}\operatorname{per}\operatorname{lb}$$
$$time_2 = rate * 4.24 \operatorname{lbs}$$
$$time_{2} = 6.56 \operatorname{hrs}$$

Theoretically.

Interesting also to note that their rate, 0.25 hrs per lb is at 325ºF and I am cooking at 170ºF at 1.5 hrs / lb or 6 times as long at 155ºF less temperature.

Prime rib using higher rack

I'm going to try to do it using convection bake mode vs roast mode to see if it will roast it more evenly. I've also put the prime rib on a higher rack to try to cook it more evenly as well. This will probably throw the time off, we'll see.

My log

Time Note
10:15 AM Put prime rib into oven set at 170ºF convection bake
1:30 PM Internal temperature hit 130ºF so removed it and foiled
4:30 PM Turn oven back on to 170ºF
4:45 PM Put prime rib back in Oven for 30 min
5:15 PM Take prime rib out and turn oven up to 550ºF
5:45 PM Put prime rib back in oven for 10 min to sear

That's only 3.25 hours, which is much shorter than the 5 hours last time and half the predicted time. Hopefully the convection heating hasn't made it tougher. My guess is that rack allowed it to warm from all directions which should theoretically make it more tender since no one side should have gotten as hot.

Turned OK. It wasn't very hot after reheating it 3 hours later. Also, I only brined it overnight and it felt like the edges were saltier than the middle. (BTW, I've been using ½ tsp / lb as a formula for dry brining. I THINK it's OK.)

Seared

Sliced

The pinkness with a pull internal temperature of 130ºF