Something to read:

http://www.jamescalhoon.com/primers_and_pressure.php

(As a note of interest, small pistol primers are .017" thick and large pistol primers are .020" thick.)

Another factor which determines the strength of a primer cup is the work hardened state of the brass used to make the primer cup. They are made with cartridge brass (70% copper, 30% zinc), which can vary from 46,000 psi, soft, to 76,000 psi tensile strength when fully hardened. Manufacturers specify to their brass suppliers the hardness of brass desired. I was not able to test primer hardness, but an educated guess says that a primer manufacturer would choose a harder brass in order to keep material thickness down and reduce costs.