I would be interested to know if there are any heuristics for how often it is the case that there is exactly one prime above $2$ in $\mathbb{Q}(\zeta_p)$, where $\zeta_p$ is a primitive $p^\text{th}$ root of unity, and $p>5$ is a rational prime.
For example, by standard Galois Theory, $2$ is inert whenever it is a generator of the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ which is believed to happen infinitely often (by Artin's conjecture on primitive roots as pointed out in the comments).
Any help would be much appreciated!