We introduce the concepts of the prime $m$-bi ideal and their associated types in the semigroups. Different characterizations of the semigroups using these $m$-bi ideals are presented. The forms of the topologies induced by the prime and strongly prime $m$-bi ideals in the semigroups are also explored. The result shows that either both the conditions of $m$-regularity and $m$-intraregularity or existence of pairwise comaximal $m$-bi ideals in a semigroup is necessary for strongly prime $m$-bi ideals to induce a topology; whereas the existence of pairwise comaximal $m$-bi ideals is necessary for the prime $m$-bi ideals to induce topology on the semigroups. We concluded that the prime $m$-bi ideals are as important to study the semigroups as the prime bi ideals.