Abstract: The mutual information for a pair of spherical regions separated a large distance can be used as a probe to characterize a CFT. For example, from the leading term in the long-distance expansion one can read the spin and conformal dimension of the lightest primary operator. Furthermore, the CFT data can also be accessed from a generalized measure involving more than two regions, the so called N-partite information. In this talk I will discuss the long distance limit of N-partite information for CFTs whose lowest-dimensional primary is a fermion. In particular, I will present a new formula for the four-partite information, and I will comment on some general features when the number of regions is odd.