# Question on essential prime implicants

I am having some trouble understand essential prime implicants. So if a minterm is not covered by another overlapping rectangle, then that is an EPI. However, if we make a K-map for $f(x,y,z)=xy+xz'+y'z$, we have minterms m4, m6, and m7 not covered by overlapping rectangles. If what I did is correct, then there should be a total of only 2 rectangles in the table-one horizontal one that completely encapsulated the 2nd row, and a vertical rectangle for the 2nd column. And so it is a rule that EPI must appear in the minimal sum of products, in which case I'd have a lot of terms, but in fact I only see that it simplifies to $y'z+x$. What am I missing here?

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Prime implicant of $f$ is an implicant that is minimal - that is, if the removal of any literal from product term results in a non-implicant for $f$ .
In your specific case (picture bellow) both of the prime implicants, $x$ and $y'z$ , are essential prime implicants also.