From Mersenne sequence to elliptic divisibility sequence, it is a important problem in number theory to prove the existence of primitive prime divisors of an arithmetically defined sequence, i.e., the finiteness of the relevant Zsigmondy set. In this paper, we prove that the Zsigmondy set defined by iteration of weighted homogeneous polynomial is a finite set. In other words, let
be a weighted homogeneous polynomial of degree
and weight
Let
and let
be the Zsigmondy set for the zero orbit
then there exists a constant
such that