While solving this question using Quine–McCluskey algorithm , I am getting total EPIs as 3 but by definition , it is giving 2 EPIs. I am attaching both solutions. Please correct me where I am wrong. 
Answer
A prime implicant is only essential if no other prime implicants can 'cover' its outputs. As you pointed out, the only prime implicants that fit this definition are the ones in the corners. The ones in the middle can be covered both by the square and by the two horizontal rectangles. So the answer is two.
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