A standard analogue clock face has numbers 1 to 12 around the edge arranged sequentially, which is nice for telling the time, but not especially interesting. It is possible to arrange the numbers in a different order so that the difference between any two adjacent numbers is prime.
For example, on the standard clock face, 3 lies between 2 and 4 and so the difference in either direction is not prime, being only 1. (For the sake of this puzzle all differences are treated as being absolute values, and so positive.) (Picture provided for completeness.)
There are many ways of doing this of course (not even counting rotations) but the specific version to be found is one that alternates prime differences around the clock-face, with one unavoidable exception. So, if you have a (cyclic) sequence [n1, n2, ... n12] the prime differences must be p1, p2, p1, p2, ... with a final, different, p0.