Category:Examples of Gaussian Primes

This category contains examples of Gaussian Prime.

Definition 1

Let $x \in \Z \sqbrk i$ be a Gaussian integer.

$x$ is a Gaussian prime if and only if:

it cannot be expressed as the product of two Gaussian integers, neither of which is a unit of $\Z \sqbrk i$ (that is, $\pm 1$ or $\pm i$)

it is not itself a unit of $\Z \sqbrk i$.

Definition 2

A Gaussian prime is a Gaussian integer which has exactly $8$ divisors which are themselves Gaussian integers.