Show that there is a disc in $\mathbb{C}$ with radius R , so that no primes of $\mathbb{Z}[i]$ are contained in the disc.
I was thinking of taking a disc which which does not touch (0,0), for example : $|z-R|+ R<|R|$
But then how does one show that this disc doesn't contain any primes in $\mathbb{Z}[i]= \mathbb{Z}+\mathbb{Z}i$.