Hi,TreblestephThe difference bettwen this two classes(a primitive recursive function and a recursive function) isusing operation of operation minimization to obtain recursive functions.

Def(recursive functions) :

--operations: superposition, Primitive recursion,minimization--functions: 0-function, S(s)-'next' function, N[n, m] - 'selec' function

Def(primitive recursive function) :

--operations: superposition, Primitive recursion

--functions: 0-function, S(s)-'next' function, N[n, m] - 'selec' function

Ackermann's function is an example of computable not a primitive recursive function