Hi frnd .
essential prime implicant is one which is not covered by any other square in the K map and it should be present in the simplified function...
In Boolean logic, an implicant is a "covering" (sum term or product term) of one or more minterms in a sum of products (or maxterms in a product of sums) of a boolean function.
prime implicant of a function is an implicant that cannot be covered by a more general (more reduced - meaning with fewer literals) implicant. W.V. Quine defined a prime implicant of F to be an implicant that is minimal - that is, if the removal of any literal from P results in a non-implicant for F. Essential prime implicants are prime implicants that cover an output of the function that no other prime implicant (or sum thereof) is able to cover.