Let $F_{n} = 2^{2^{n}} + 1$, where $n > 0$.

Pepin's Test asserts that $F_{n}$ is prime if and only if $F_{n} \mid 3^{\frac{F_{n} - 1}{2}} + 1$.

QUESTION: What is the big-$\mathcal O$ complexity of this test if it is implemented in an algorithm with ``repeated squaring''?

ALSO: Are there any other tests for determining the primality of a Fermat number more efficient than Pepin's Test?