Solution
= Solution
Assume a complete list $f$ were primitive recursive. Closure under diagonal composition and successor makes
$$
d(k)=f(k,k)+1
$$
primitive recursive. Completeness gives a row $n$ with $f(n,k)=d(k)$ for every $k$, but at $k=n$ this says $f(n,n)=f(n,n)+1$. This is the <diagonal argument>.