Ackermann Function primitive recursive I am reading the wikipedia page on ackermann's function, http://en.wikipedia.org/wiki/Ackermann_function
And I am having trouble understanding WHY ackermann's function is an example of a function which is not primitive recursive.
I understand that the ackermann function terminates, and thus is a total function. So why is it not primitive recursive? The only information that i can find on the wikipedia page is 

[Ackermann's function] grows faster than any primitive recursive function and is therefore
  not primitive recursive

Which isn't a good example of why it is not primitive recursive.
Could anyone explain to me how exactly ackermann's function is NOT primitive recursive please?

The intuitive reason for why it is not primitive recursive is that it is recursing on more than one parameters, the primitive recursive functions are defined by functions recursing on only one parameter. 
It is more complicated to show that a function is not a primitive recursive because we have to prove than no primitive recursive function will compute the same function, i.e. the fact that the definition of Ackermann function is not explicitly primitive recursive doesn't mean that there is no primitive recursive way of computing the same function. And the easiest way to show this cannot happen (AFAIK) is to show that it grows faster than any primitive recursive function so it cannot be one of them.
There is a hierarchy for recursive functions using recursion similar to primitive recursion but with more parameters. IIRC, Ackermann function is in the second level (taking primitive recursive functions to be the first level), i.e. can be computed by recursion on two parameters.
