OK, bear with me. One of my favorite 1990s movies is Contact, a largely-forgotten film where Jodie Foster and Matthew McConnaughey work through thorny questions of existence with the help of special effects and messages from aliens. The movie is based on the Carl Sagan novel of the same name, which eschews special effects (since it is a book) and adds in several helpings of cosmology, philosophy, and physics.
I don’t want to terribly spoil either the movie or the book for you but I do have to tell you that one way the book differs from the movie is that finally at the end, the book shows you that there is some sort of overarching intelligence to the universe (whether or not you call it a deity) while the movie sort of leaves things hanging. It has to do with the way pi looks after millions and millions of digits… it starts to behave in a way that’s very predictable and obviously due to intelligence.
So I was thinking about this old movie and even older book when I recently read that according to Gizmodo, the distribution of prime numbers isn’t as random as we thought. There’s a distinctly non-random pattern to the distribution of the last digit in prime numbers, at least in the first couple hundred of them. This sounds like a really dry subject, and even the article admits that it’s probably meaningless. After all, randomness isn’t what you think it is; it doesn’t mean that you can’t roll the dice 10 times and get 7 every time. It actually means that the odds of your doing that are precisely the same as your odds of getting any other specific combination, and there are a lot of possible combinations. (By the way, your odds of hitting any specific combination of dice is slightly higher than 60 million to 1, I think. Maybe someone will check my math.)
So maybe the distribution of prime numbers doesn’t mean anything. Maybe it’s just a random happenstance that doesn’t mean anything. Or, maybe it’s aliens trying to tell us something, like a cosmic IQ test. If you as a society are smart enough to figure this out, give us a call. That sort of thing. I suppose we’ll know soon enough if we get a cosmic call from far beyond.