This is Normal Form Theorem (Second Edition of Computability, Complexity, and Languages written by Martin Davis page 75):
Let $f(x_1,...,x_n)$ be a partially computable function. Then there is a primitive recursive predicate $R(x_1,...,x_n,y)$ such that:
$f(x_1,...,x_n) = L(min R(x_1,...,x_n,z)_z)$ (minimization is on z)
So I think an immediate result of this theorem is that every partially computable function is primitive recursive and every primitive recursive function is partially computable. is it true?