Primitive Recursive Function is URM Computable

Theorem
Every primitive recursive function‎ is URM computable.

Proof
This follows immediately from:
 * The fact that the basic primitive recursive functions are URM computable;
 * Functions obtained by substitution from URM computable functions are URM computable;
 * Functions obtained by primitive recursion from URM computable functions are URM computable;
 * The definition of primitive recursive function‎.

Note
This does not mean that every URM computable function is necessarily primitive recursive.