Unramified (rational) prime of a number field (reviewed)

A unramified (rational) prime of a number field $K$ is a prime integer $p$ such that the ideal generated by $p$ is factored into distinct prime ideals in the ring of integers $\mathcal{O}_K$ of $K$ $$p\mathcal{O}_K = \mathcal{P}_1\cdots \mathcal{P}_k.$$

The unramified primes of $K$ are the primes which do not divide the discriminant of $K$.