I've recently been reading 'The Music of the Primes' by Marcus du Sautoy. Being still at school, I can't really fully understand the whole problem, let alone solve it, but I have had a couple of thoughts:
1. Has anyone ever looked at non-primes, because if some of them are on the line it may not be as useful.
2. Has anyone thought of looking at the area (or volume) under the graph, for example between neighbouring zeroes?
I apologise if these have been thought of already, but if not, I hope that they provide some headway into the problem, or some enjoyment in trying them out.