I'm trying to use the Finite Fields package to show that $x$ is not a primitive element of $\mathbb{Z}_3[x]/\langle x^3 + 2x + 2 \rangle \cong GF(3^3)$. The idea is to take the following piece of code:
i = 1;
While[ReduceElement[GF[3, {2, 2, 0, 1}][{0, 1, 0}]^i] !=
ReduceElement[GF[3, {2, 2, 0, 1}][{1}]], Print[i]; i++]
which should compute all the powers of $x$ and terminate when it reaches the identity. However, it does not produce any output; I even inserted the Print statement to make sure it would at least do something, but I still get nada. What is going on here? How can I make this piece of code work the way it's supposed to?