A combinational logic circuit takes a $4$-bit unsigned binary integer number at its inputs labeled $\mathrm{D}_{3}, \mathrm{D}_{2}, \mathrm{D}_{1}$ and $\mathrm{D}_{0}$, where $\mathrm{D}_{3}$ is the most significant bit. For decimal input $1,2,3,5,7,11$ and $13,$ the output $S$ is to be at logic $1,$ and it is to be at logic $0$ otherwise.
How many prime implicants does $S$ have which are not essential prime implicants?
