In the power set Boolean algebra $\mathcal{P}(\mathbb{N})$, a subset $I \subseteq \mathcal{P}(\mathbb{N})$ is an ideal if $\emptyset \in I$, it is closed under unions, and any subset of an element in $I$ is also in $I$. An ideal $I$ is prime if $I \neq \mathcal{P}(\mathbb{N})$ and for all $A, B \subseteq \mathbb{N}$, if $A \cap B \in I$ then $A \in I$ or $B \in I$. Which of the following subsets of $\mathcal{P}(\mathbb{N})$ is a prime ideal?