 Total computable diagonal over primitive recursive syntax

Enumerate all valid unary primitive recursive functions in intension by their decidable codes $p_n$, and interpret each extension $F_{p_n}$. The function $d(n)=F_{p_n}(n)+1$ is a total computable function, since each finite construction terminates. If it were primitive recursive, some $F_{p_j}$ would equal $d$, giving $d(j)=d(j)+1$. Repeated extensions in the syntax enumeration do not affect this argument.