In Boolean algebra, a prime implicant is a product term that cannot be further reduced by combining it with another term. On a Karnaugh map, it represents a maximal rectangular group of adjacent cells (1s for sum-of-products, 0s for product-of-sums). Identifying all prime implicants is the core step in finding the simplest, most efficient logic gate implementation for a circuit.
You missed a prime implicant in the corner cells, which is why your logic expression has an extra gate.
Related terms
Essential prime implicant
A grouped term in Boolean logic minimization that covers at least one output state no other group can cover.
Non-essential prime implicant
A grouped logic term in a Karnaugh map whose outputs are entirely covered by other groupings.
Combinational logic
A type of digital logic where outputs are determined entirely by the present combination of inputs.