I don't understand what that graph is showing. Which variable is independent, or supposed to be? It can't be buckets as a function of collisions. At first I thought he had his axes reversed (from the customary y as a function of x), but it's not a graph of collisions as a function of buckets, either, because reading it that way implies that a very small number of buckets produces a small number of collisions, which is obviously false with a hundred million inputs being distributed over ten or less buckets.
It looks like a graph of the moral equivalent of 1=1, by numeric methods. What am I supposed to see there?
It's a histogram. It's counting the number of buckets (y axis) for each number of collisions (x axis). He's showing that the distribution is the same for both methods; if one had a clear advantage, it should have a relatively more uniform distribution.
The problem is that the input distribution is uniform, so you'd expect a pretty decent distribution of collisions regardless of what your modulus was. A prime modulus only helps for non-uniformly distributed inputs.
It looks like a graph of the moral equivalent of 1=1, by numeric methods. What am I supposed to see there?