Here's an interesting fact, looking at quads, (i.e. two sets of twins in a space of 9), the difference between two sets of quads must be a multiple of 30. However, differences cannot be 30*x, when x= 2mod7 or 5mod7, for some reason that a mod specialist will be able to explain.
The run of quads in the range 5 to 1e9 produces x of values between 1 to 13184.
