> There is a set of rules for determining primes in the
> Gaussian integers
> based on primes in the integers, but it has been awhile since I've
> looked at them and I don't have the book handy.
The Gaussian primes are 1+i (and associates); integer primes of the form
4n+3 (and their associates) and the factors of integral primes of the form
4n+1. The latter can always be expressed as a^2+b^2 and so their
factorization into Gaussian primes is (a+bi)(a-bi).
The "smallest" Gaussian primes (i.e. the ones of smallest modulus) are
1+i, 3, 2+i, 7, 11, 8+i, 19, 23, 5+2i, ... and their associates.
Paul
