%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Abstract: Is the Ackermann functional optimal? A standard construction, originally due to Ackermann, produces a function that is clearly recursive in some sense but can be shown to be not primitive recursive. This construction can be relativized to produce a jump in the poset of degrees up to primitive recursive equivalence. What happens between a degree and its Ackermann jump? I will give some information on this question, and try to make the talk as boring as possible. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%