Show that each of the ideals $I_k=\langle x_1,...,x_k\rangle$ in $F[x_1,...,x_n]$ for $1\leq k \leq n$ are prime and that each power is primary
Any power of $(X_1, X_2,...,X_i)$ is primary in $k[X_1, X_2,...,X_n].$