  Close to charge neutrality, the low-energy properties of high-quality
suspended devices based on atomically thin graphene layers are determined by
electron-electron interactions. Bernal-stacked layers, in particular, have
shown a remarkable even-odd effect with mono- and tri-layers remaining gapless
conductors, and bi- and tetra-layers becoming gapped insulators. These
observations $-$at odds with the established notion that (Bernal) trilayers and
thicker multilayers are semi-metals$-$ have resulted in the proposal of a
physical scenario leading to a surprising prediction, namely that even-layered
graphene multilayers remain insulating irrespective of their thickness. Here,
we present data from two devices that conform ideally to this hypothesis,
exhibiting the behavior expected for Bernal-stacked hexa and octalayer
graphene. Despite their large thickness, these multilayers are insulating for
carrier density |n|<2-3x10$^{10}$cm$^{-2}$, possess an energy gap of
approximately 1.5 meV at charge neutrality (in virtually perfect agreement with
what is observed in bi and tetra layer graphene) and exhibit the expected
integer quantum Hall effect. These findings indicate the soundness of our basic
insights on the effect of electron interactions in Bernal graphene multilayers,
show that graphene multilayers exhibit unusual and interesting physics that
remains to be understood, and pose ever more pressing questions as to the
microscopic mechanisms behind the semimetallic behavior of bulk graphite.
