Need some help...

Let $\displaystyle \mathbb{Z}[\sqrt{-5}]$ the ring of gaussian integers.

1)Show that $\displaystyle <3>=<3;1+\sqrt{-5}><3;1-\sqrt{-5}>$

($\displaystyle <a>$ means the ideal generated by $\displaystyle a$)

2)Prove that the ideal on the right is prime.

Thank you folks!