A family ${\cal S}\subseteq{\cal P}(\omega)$ is *intersecting* if any two members of ${\cal S}$ have non-empty intersection. Zorn's Lemma implies that every intersecting family is contained in a maximal intersecting family with respect to set inclusion $\subseteq$.

Every ultrafilter on $\omega$ is maximal intersecting. Let ${\frak U}$ be the collection of ultrafilters on $\omega$, and let ${\frak M}$ be the collection of maximal intersecting families on $\omega$. We have ${\frak U}\subseteq {\frak M}$ and $|{\frak U}| = 2^{2^{\aleph_0}}$.

**Question.** Is $|{\frak M}\setminus{\frak U}| = 2^{2^{\aleph_0}}$?