Based on the minimal and simple representations, we introduce two types of Jacobson semisimplicity, $m$-semisimplicity and $s$-semisimplicity, of a semiring $S$. Every $m(s)$-semisimple semiring is a subdirect product of $m(s)$-primitive semirings. It is shown that a commutative $s$-primitive semiring is either a two element Boolean algebra or a field. Every $s$-primitive semiring is isomorphic to a 1-fold transitive subsemiring of the semiring of all endomorphisms of a semimodule over a division semiring.