TITLE: Is each power of a prime ideal a primary ideal?
QUESTION [17 upvotes]: I want to show that each power of a prime ideal is a primary ideal or I have to think about a counterexample?

REPLY [2 votes]: One may even find such an example in the polynomial ring $k[x,y,z]$: the ideal $I=\langle x^3-yz, y^2-xz, z^2-x^2y\rangle$ is prime but $I^2$ is not primary as explained in Northcott, Ideal Theory, Example 3, p. 29.