> 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.
It's been pointed out to me that (8+i) is composite, with factorization
8 + i = (2 - i) * (3 + 2*i).
Oops! That's what comes of performing factorizations in my head and without
checking before posting. I meant, of course, 4+i. For some bizarre reason,
I divided 16 by 2, rather than taking its square root.
I also omitted the prime factors of 13 (3+2i and associates) from the list.
My apologies for spreading misinformation.
Paul
