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?

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?