I take it, then, that you find nothing inspirational in the videos made by Vi Hart either. To each, their own. As to the diagrams you pointed me at, they mean

I take it, then, that you find nothing inspirational in the videos made by Vi Hart either. To each, their own. As to the diagrams you pointed me at, they mean nothing to me, and do not inspire me. If I knew more about number theory, perhaps they would. Some things are not about information, they are about inspiration. The visualization in the OP provides inspiration that number theory is connected to other fields of math. You can see structure in the way that the periodic curves intersect and the primes are the gaps. If you could understand that structure, then maybe you could understand the gaps. Then again maybe not. That doesn't mean that the question and the visualization doesn't cause you to think and wonder. Sure, this is old hat to mathematicians, and for all I know, this approach is a complete dead end. Sometimes dead ends are interesting too.