Here's what I did so far:

I try to find GCD .

Firstly, I find GCD

GCD

Next, GCD

So GCD

Now I check is (-1-i) irreducible.

So in any case, one of them is +-1, which means that (-1-i) is irreducible, so (1+3i, 3+11i, -1-11i) is generated by an irreducible element so it is prime.

I'm pretty sure I made mistakes, could someone please correct me?