  We prove the finiteness of the Zsigmondy set associated to the critical orbit
of f(z) = z^d+c for rational values of c by finding an effective bound on the
size of the set. For non-recurrent critical orbits, the Zsigmondy set is
explicitly computed by utilizing effective dynamical height bounds. In the
general case, we use Thue-style Diophantine approximation methods to bound the
size of the Zsigmondy set when d >2, and complex-analytic methods when d=2.
