Temporal complexity – Why was it thought that the test of primality was NP?

To check if $$n$$ is first, just try to divide $$n$$ in number up to $$sqrt {n}$$, which means that the complexity would be $$O ( sqrt {n})$$. In my opinion, $$O ( sqrt {n}) so this simple algorithm is already P. But why did people think that the primality test is NP and were surprised by the AKS primality test?