Algorithm to determine whether a power of a prime ideal is primary in a polynomial ring over a field

Question

Let $P$ be a prime ideal of a polynomial ring $k[X_1,\cdots, X_m]$ over a field $k$. Suppose a finite basis of $P$ is given. Is there an algorithm to determine whether $P^n$ is primary for a given positive integer $n$? If yes, what is it?