  We consider the problem of enumeration of primitive TSRs of order n over any
finite field. Here we prove the existence of primitive TSRs of order two over
binary field extensions. Moreover we give a general search algorithm for
primitive TSRs of odd order over any finite field and in particular of order
two over fields of characteristic 2. We also give certain bounds on the number
of primitive TSRs in special cases and propose a conjecture regarding the
existence of certain special type of primitive polynomials, which answers the
existence of primitive TSRs of odd order n over Fqm and primitive TSRs of order
greater than 3 over binary field extensions..
