Does anyone have a larger list of the first unique gaussian primes ordered by their norm? Uniqueness can be achieved if one starts with $p_1=1+i$ and requires that for odd primes $p_i \equiv 1 \mod 2+2i$. The first primes are then \begin{align} p_2 &= -1 + 2i \\ p_3 &= -1 - 2i \\ p_4 &= -3 \\ p_5 &= 3 + 2i \\ p_6 &= 3 - 2i \\ p_7 &= 1 + 4i \\ p_8 &= 1 - 4i \\ \vdots \end{align}
Also: Is there something like a prime-number theorem for gaussian primes?