  We show that there is a fermionic minimal model, i.e. a 1+1d conformal field
theory which contains operators of half-integral spins in its spectrum, for
each $c=1-6/m(m+1)$, $m\ge 3$. This generalizes the Majorana fermion for
$c=1/2$, $m=3$ and the smallest $\mathcal{N}{=}1$ supersymmetric minimal model
for $c=7/10$, $m=4$. We provide explicit Hamiltonians on Majorana chains
realizing these fermionic minimal models.
