$2=(1+i)(1-i)$ what does that imply in $\mathbb{Z}[i]$?

Question

In the ring $\mathbb{Z}[i]\ $ $\ \ 2|(1+i)(1-i)=2$ but $2\nmid (1\pm i)$

So is $2$ not prime (or is it prime but irreducible) in $\mathbb{Z}[i]$ or is $\mathbb{Z}[i]$ not a unique factorization domain?