The world's largest prime number — visualized

Philip Bump took the recently discovered 17-million-digit prime number and, six digits at a time, converted it into RGB colors. This is the result.

Maggie Koerth-Baker is the science editor at BoingBoing.net. She writes a monthly column for The New York Times Magazine and is the author of Before the Lights Go Out, a book about electricity, infrastructure, and the future of energy. You can find Maggie on Twitter and Facebook.

Maggie goes places and talks to people. Find out where she'll be speaking next.

MORE: art • math • prime numbers • Science

More at Boing Boing

Eurovision 2013: An American in London

The technology that links taxonomy and Star Trek

http://profiles.google.com/spockosemail Mr. Spocko

Hey, I can see my house!
http://www.youtube.com/user/Freethinkersanon Christopher

They’re heeerrrrre…
http://www.facebook.com/marko.raos Marko Raos

No, it’s not. It’s JPEGed. Plz replace with original bitmap for my geek pleasure. :)
- atteSmythe
  
  The ‘original’ size on Flickr is a PNG
Samuel Valentine

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.
blurgh

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.
- http://memoid.tumblr.com/ memoid
  
  The way they did it means no pixel can be brighter than #999999, did I get that right?
  - 3eff_jeff
    
    It’s a Mersenne Prime. The hexadecimal representation of a Mersenne Primes is very boring. It would be a white canvas with no more than two not-white pixels in opposite corners.
    - Marius van Voorden
      
      Hmpf, you’re right.
      
      But it would still be neater >:(
      - 3eff_jeff
        
        Well, look at this way: Maggie posted both at the same time. One in the body of the post and one as the background…
    - joshhaglund
      
      Seems that’d illustrate the Mersenne Prime – ness of the number. Which would help people understand math. Instead, everyone just sees noise and thinks magic eye.
    - Selena60
      
      You young fellows and your fancy math. Where’s the kittens? They promised me kittens!
      - http://lemoutan.blogspot.com/ Lemoutan
        
        But primes!
Judonerd

…… Congratulations?
http://deansli.st/ Dean Putney

With just the right processing, it turns out that all the prime numbers are magic-eye images of absurdly happy puppies.
- awjt
  
  Dude, what’s wrong with mine? I see Hitler kissing Beyoncé?!
  - Antinous / Moderator
    
    I see Santa Claus riding a shark.
    
    I always see Santa Claus riding a shark.
    - awjt
      
      Thank God it’s not the Pope.
      - Felton / Moderator
        
        I see a shark riding the popemobile.
      - awjt
        
        We almost have enough characters for the cast of The Last Supper. Too bad the comments have run out.
      - http://lemoutan.blogspot.com/ Lemoutan
        
        That’s it then. The shark jumped the primate.
- http://www.nogunarmy.com/ monstrinho
  
  I see Optimus PRIME! (sad trombone sound)
- niktemadur
  
  On top and slightly left of center, a cuddly lion wearing spectacles! No wait, he’s cool and they’re Ray-Ban Wayfarers… oh never mind.
http://www.facebook.com/people/David-Horton/100001980195134 David Horton

Shooped. Can tell by the pixels.
http://maggiekb.com/ Maggie Koerth-Baker

Stare at it long enough, and you’ll see a sailboat. Promise.
- Fef
  
  I saw Math Jesus.
- http://www.facebook.com/people/Andrew-Clark/1069589844 Andrew Clark
  
  Wow! It’s a schooner!
- http://www.facebook.com/people/David-Horton/100001980195134 David Horton
  
  It’s a SCHOONER!
- niktemadur
  
  Now that you mention it, I’m getting a LOT of texture there, fluctuating between Hindu and Mayan, very elegant.
remainzz

What other ways can it/has it been visualised?
- http://www.facebook.com/people/David-Horton/100001980195134 David Horton
  
  One girl saw the virgin mary’s toast.
- retchdog
  
  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.
http://twitter.com/tadasyoyolt Tadas Jelinek

Fun fact: convert to it to binary and all digits will be 1. Why? Because it’s 2^n -1
- retchdog
  
  And there will be a prime number of 1s. Why? Because it’s 2^p-1.
joshhaglund

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
  
  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).
- https://launchpad.net/~zak-mckracken Zak McKracken
  
  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…
timquinn

How do we know it isn’t just random? Because it is!
- http://www.facebook.com/people/Skip-Nordenholz/100003613616195 Skip Nordenholz
  
  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
    
    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.)
http://twitter.com/Arduenn Arduenn

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.
http://twitter.com/ClintonD Clinton

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
http://www.facebook.com/people/Skip-Nordenholz/100003613616195 Skip Nordenholz

World’s largest prime number, how far away is this from the worlds largest number?
- AnthonyC
  
  This is the largest *known* prime. There is no largest prime, nor a largest number. So, infinitely far.
  
  But if you’re curious about how big finite numbers can get and still be, in some sense, useful, then see
  http://en.wikipedia.org/wiki/Graham's_number
  - http://profiles.google.com/stephen.mcgreal Stephen McGreal
    
    http://www.youtube.com/watch?v=4J9MRYJz9-4
    - http://twitter.com/beep54orama B E Pratt
      
      Ooooo, computerized toast! I’m in!
knappa

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.)
niktemadur

Ad Reinhardt got it right fifty years ago, without the aid of all your fancy schmanzy computing.
http://1.bp.blogspot.com/-ETungHt-fEI/TiKUX_3kDjI/AAAAAAAAEos/J1IbauV9fqM/s1600/1961+Abstract+Painting+No.+4.jpg
http://www.nogunarmy.com/ monstrinho

if i increase the contrast slightly i get this…uh oh.
http://i50.tinypic.com/2ahbdk4.jpg
- Brent Kirkham
  
  Dad?
superherodude

That’s exactly how I thought it should look!