  There is much interest in the realization of systems with p-wave pairing in
one dimension or chiral p-wave pairing in two dimensions, because these are
believed to support Majorana modes at the ends or inside vortices. We consider
a two component system of composite fermions and provide theoretical evidence
that, under appropriate conditions, the screened interaction between the
minority composite fermions is such as to produce an almost exact realization
of p-wave paired state described by the so-called anti-Pfaffian wave function.
This state is predicted to occur at filling $\nu=3/8$ or 13/8 in GaAs when the
Zeeman energy is sufficiently small, and at $\nu=\pm 3/8$ or $\pm 13/8$ in
single layer graphene when either the Zeeman or the valley splitting is
sufficiently small.
