Ackermann function or Ackermann-Peter function is a simple example of a recursive function that is not primitive recursive. It takes two natural numbers as arguments and yields a natural number, and its value grows extremely quickly. Even for small inputs (4,3, say) the values of the Ackermann function become so large that they cannot be feasibly computed, and in fact their decimal expansions cannot even be stored in the entire physical universe. (https://academickids.com/encyclopedia/index.php/Ackermann_function)