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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 uniformly bounding the size of the Zsigmondy set for alland all  d ≥2. We prove further that there exists an effectively computable bound  M ( c ) on the largest element of the Zsigmondy set, and that, under mild additional hypotheses on  c , we have  M ( c )≤3.

Primitive Prime Divisors in the Critical Orbit of z d + c