It's like there is this long, infinite road and along this road are mile markers and every so often one of these mile markers has a rest stop at it. Mile marker 3, 5, 9, and so on. The farther your drive however the more you notice how spread out these rest stops are, eventually having thousands upon thousands of miles between them. Then, as in this article, you discover a pack of six rest stops very close to each other when all the other ones were thousands of mile markers apart. Thats probably the closest I can get this to a car analogy.
There are rest stops at 2, 3, 5, 7, 11, 13, and so on, but 9 is not a rest stop. The first two overlapping sets of six rest stops aren't spaced the same as the rest, and thus don't have the same mathematical properties. The Riecoin compliant prime sextuplets, err, I mean rest stops on the infinite highway are {7, 11, 13, 17, 19, 23} and {97, 101, 103, 107, 109, 113}, except they are too small for cryptography.