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Infographic: Visualizing Prime Numbers, For People Who Suck At Math

Numbers hide complex relationships that are tough to imagine. So here’s a pretty picture that brings them to light.

The world belongs to the mathematicians and the physicists. We lay people may pump our minds with Discovery Channel specials, but they’re the ones who get to understand how it all really works—how the numbers add up into atoms and stars and gravity. Well…usually.

Click to enlarge.

Jason Davies, a data visualization specialist and computer scientist, created a graphic for the rest of us to picture the unique relationships between prime numbers. For those who don’t remember, prime numbers are the special numbers divisible only by 1 and themselves. 2, 3, 5 and 7 are all primes, while 4 (since it’s also divisible by 2) doesn’t make the cut.

In his visualization, you can highlight any natural number (the normal numbers we count) on the number line and see how it relates to its fellow numbers. The wavy lines are divisors (numbers that divide evenly into other numbers). So 11 is marked as a prime number—a number only divisible by 1 and itself. And when you highlight 11, you’ll see its waveform, which flows through 11, then 22, then 33 (and so on). It’s an interesting relationship to behold, especially when you highlight 11’s neighbor, 12.

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When highlighting 12, we see all sorts of other divisors that are related to this number. Waveforms that begin at 2, 3, 4 and 6 all intersect, as this highly divisible number becomes a interlinked in a chain with all of its compatible friends.

As a math deficient liberal arts major, I asked Davies if his visualization offers us a glimpse into how he "sees" numbers, a peek behind the curtain of a mathematical mind. Interestingly enough, it’s not how he normally sees numbers at all.

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"I must admit, I hadn’t thought of visualising the number line in this way prior to creating this. So it’s probably not how most mathematicians "see" the number line, or primes," Davies tells me. "But it’s incredibly interesting, even for hardcore math geeks, because it allows you to explore the compositeness of a whole set of numbers all at once. You don’t have to type a number into a box and press a button; you can just see a number and its neighbours all together simply by moving a mouse."

It’s a salient point. In school, we learn to calculate numbers by hand, and these calculations are fundamentally, always about relationships between the numbers. But how often were we shown these relationships or the visual consequences of these relationships? It’s no wonder why so many people say geometry was their favorite math class: The numbers become something they can actually see. Case in point, I took a year of trigonometry from a teacher who never once uttered the word "triangle."

[Ha tip: Infosthetics]

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  • Glenn Westmore

    Some interesting facts and puzzles about Prime Numbers and Magic Squares, Smith Numbers, and Arithmetic and Palindromic Primes on this blog:

  • Hannah Thomas

    Love this!  Thanks so much for posting it. Dubba's got a great idea!  I'd like to see that too.  
    You might want to know your Pin This button didn't work- I had to pin it manually.  Do I recognize a Squarespace powered website here?  Supercool- I'm so glad I stumbled across this and I'm amazed I haven't come across it before now.

  • PBJ

    Small mistake in the first paragraph:

    "1, 2, 3, 5 and 7 are all primes, while 4 (since it’s also divisible by 2) doesn’t make the cut."1 is not a prime number as a prime is defined as greater than 1.

  • PBJ

    Mark, no problem. Interesting article.

    Brian, I like that definition better as well.

  • johnseiferth

    Just noticed that the book/movie Contact was therefore wrong. When the alien space broadcast is restarting it's sequence, it begins with 1. Which by definition, is not a prime. Interesting.

  • Brian Clare

    Agreed, but I'm not sure i like your definition of prime. A good definition is "a number with exactly two positive integer divisors". Then 1 is not prime because it has only one divisor