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?

Here's a proof showing why Ackermann's function is not primitive recursive.

The key to showing that A is not primitive recursive, is to find a properties shared by all primitive recursive functions, but not by A . One such property is in showing that A in some way ``grows'' faster than any primitive recursive function

Also, here's a proof showing that Ackermann's function is both a total function and a recursive function.
