The world's largest prime number — visualized


51 Responses to “The world's largest prime number — visualized”

  1. Mr. Spocko says:

    Hey, I can see my house!

  2. Christopher says:

    They’re heeerrrrre…

  3. Marko Raos says:

    No, it’s not. It’s JPEGed. Plz replace with original bitmap for my geek pleasure. :)

  4. Samuel Valentine says:

    Well great. You spend all day workin’ real hard and then you gaze into an image of the very soul of madness and doom.

    Guess it’s the cults for me again.

  5. blurgh says:

    Bah. They should have written the number in hexadecimal, taken 6-digit chunks, and then rendered that as an image. It’s a bit neater that way.

  6. Judonerd says:

    …… Congratulations?

  7. Dean Putney says:

    With just the right processing, it turns out that all the prime numbers are magic-eye images of absurdly happy puppies.

  8. David Horton says:

    Shooped. Can tell by the pixels.

  9. Stare at it long enough, and you’ll see a sailboat. Promise. 

  10. remainzz says:

    What other ways can it/has it been visualised?

    • David Horton says:

      One girl saw the virgin mary’s toast.

    • retchdog says:

      I don’t know of any visually-available structure in a given prime number (apart from the stuff about mersenne primes being 2^p-1 of course). afaik, there’s no really good reason to think there will be any, and arguably a good reason to think there isn’t any.

      I failed at math and am now a statistician, so the following may be completely wrong:

      Although there are reasons we sort of know the average size of the “step” from one prime number to the next, the same knowledge (assuming the Riemann hypothesis) also implies that the _actual_ step size between any two adjacent primes will be very chaotic.

      Think of it as knowing the distance of a flight from SF to NYC in miles, versus knowing it in inches. The former won’t help with the latter at all, even though they’re related.

      Since an interesting visualization of a prime will (probably?) be very sensitive to the exact step size, the chaos is a vague reason to think there won’t be one.However, if you look at the _overall_ distribution of primes it can be both cool and mathematically interesting. Google will give you several examples.

  11. Fun fact: convert to it to binary and all digits will be 1. Why? Because it’s 2^n -1

  12. joshhaglund says:

    I can’t help but wonder where the padding is, to fit within 1726 * 1666 * 6 pixels (because it’s a prime number, it shouldn’t divide cleanly). Also, if there are only 2 digits per RGB value, there’s a lot of color space wasted. I can’t do the math now, but seems like it should be converted to hexadecimal first.

    • LintMan says:

      You can easily scale the 00-99 up to the 8-bit 0-255 range to make 24-bit color RGB values. 

      As others have said, the hex representation would be very boring since it’s a 2^k-1 prime (ie: All FF’s).

    • What needs to divide cleanly into 1726x1666x6 is the number of digits, not the number itself.
      According to wikipedia, the number has 17,425,170 digits, but the image only uses 17,253,096, which leaves 172,074 digits unaccounted for … I wonder if that couldn’t have been done better. Or maybe he did after all use more than 6 digits per pixel to fill the remaining space?
      If I do a prime factor decomposition, I get 6* 3*5*7*17 * 1627 (which appears to be a prime number)
      So logically, the dimensions 1785*1627 would seem more appropriate. Unless I just made a mistake…

  13. timquinn says:

    How do we know it isn’t just random? Because it is!

    • True randomness can only be described by repeating every random bit, it con not be reduced. This isn’t randomness because it can be describe as 2^k-1, which is much simpler.

      • Tynam says:

        Exactly.  Truly random things don’t have short-form representations.

        (They can act random though.  Pi passes every meaningful test for randomness, except that it’s not in any way random.)

  14. Arduenn says:

    Now why didn’t they choose an aspect ratio, such that there wouldn’t be an ugly black line at the end? After all, a prime number can’t end with a bunch of zeroes.

  15. Clinton says:

    I think I read a book about thi…en-lil lugal kur-kur-ra ab-ba dingir-dingir-re-ne-ke inim gi-na-ni-ta nin-ĝir-su šara-bi ki e-ne-sur

  16. World’s largest prime number, how far away is this from the worlds largest number?

  17. knappa says:

    In the spirit of things, I just did something similar with the 33rd Mersenne prime (in wikipedia’s list) The two images encode the magnitude of the digits of 2^(859433)-1 in base 13 and 17. The computer is still chugging away at rendering an image for 2^(57885161)-1 in base 919 (A large base reduces the size of the image.)

  18. niktemadur says:

    Ad Reinhardt got it right fifty years ago, without the aid of all your fancy schmanzy computing.

  19. monstrinho says:

    if i increase the contrast slightly i get this…uh oh.

  20. superherodude says:

    That’s exactly how I thought it should look!

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