The term partial recursive function is often used in a general sense to mean any computable function on the natural numbers defined by a model of computation. However, strictly speaking, a partial recursive function is simply a function defined by primitive recursion and Kleene's μ-recursion scheme (see minimization). Not all such functions are total functions since the use of the μ-operator allows the possibility of nontermination.
A primitive recursive function, however, cannot involve the μ-operator and is hence guaranteed to be total. The Ackermann function is the standard example of a total recursive function that is not primitive recursive.