Contact and Prime Numbers

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.

What this has to do with anything…

So I was thinking about this old movie and even older book when I came across a five-year old article. You see, 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.)

Randomness in daily lives

Our lives are full of randomness and pseudo-randomness. Pseudo-randomness is what happens when you shuffle your Spotify playlist. Computers are not truly capable of generating random lists or even random numbers. It seems like they are because they do a good job of it. But the world of computers is an ordered one. The appearance of randomness comes from the fact that so much is happening at once that you’re likely to get an unexpected result from asking for a number at any moment. No matter how planned the “random number generator” is, using it a few times will not show its randomness. On the other hand, ask your computer to generate 500,000 random numbers in a row and the numbers it generates will have a pattern. That pattern comes from the program used, not from some sort of divine guidance.

Getting way too philosophical

I’m not sure what that has to do with daily life, but there’s definitely something there. It’s probably too deep for this blog to deal with. 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.

About the Author

Stuart Sweet
Stuart Sweet is the editor-in-chief of The Solid Signal Blog and a "master plumber" at Signal Group, LLC. He is the author of over 8,000 articles and longform tutorials including many posted here. Reach him by clicking on "Contact the Editor" at the bottom of this page.