The class number is an important term from algebraic number theory. It specifies the order of the class group of an algebraic number field $K$ and can be interpreted as the number of different ways to factorize an element of $K$ into prime elements. If the class number is equal to $1$, the $K$ is called a unique factorization domain, e.g. the integers $\mathbb{Z}$. It is long known that for imaginary quadratic fields the class number is $1$ only for the values: $$K = \mathbf{Q}(\sqrt{d}), d \in \{-1,-2,-3,-7,-11,-19,-43,-67,-163\}$$ There are a surprisingly large number of ways to compute the class number of a quadratic field, which i want to show you next.