  Notice that \(D\) is a total, computable function from \(\mathbf{N}\) to \(\mathbf{N}\), but it is not primitive recursive. Why? Suppose for the sake of a contradiction that \(D\) were primitive recursive. Then \(D\) would be equal to \(p_{d}\) for some \(d\in \mathbf{N}\). But it would then follow that