impressive solution!
I tried a direct attack with the symbolics and it fails ("no solution found") but at least it could verify the solution you found.
So I guess a brute force approach using a loop testing all multiples of 3 evaluated symbolically may come up with the solution - but probably not in a lifetime.
Apropos time - the result is the same in real Mathcad (V.15) but the difference in calculation time compared to Prime is quite remarkable!
Prime 11:
Mathcad 15:
But of course, symbolics makes it easier to arrive at the solution using your thoughts:
