I'd like to correct a slight booboo in my previous. There's no change to the a^3 + b^3 = 22c^3 solution. But below in the Pythagorean problem, I used 'a' and 'b' for two different purposes. See below.
17,299^3 + 25,469^3 = 22(9,954^3), both 17,299 and 25,469 are prime.
I, too, stumbled...