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.

# The world's largest prime number — visualized

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art, math, prime numbers, Science

Hey, I can see my house!

They’re heeerrrrre…

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

The ‘original’ size on Flickr is a PNG

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.

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.

The way they did it means no pixel can be brighter than #999999, did I get that right?

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.

Hmpf, you’re right.

But it would still be neater >:(

Well, look at this way: Maggie posted both at the same time. One in the body of the post and one as the background…

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.

You young fellows and your fancy math. Where’s the kittens? They promised me kittens!

But primes!

…… Congratulations?

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

Dude, what’s wrong with mine? I see Hitler kissing Beyoncé?!

I see Santa Claus riding a shark.

I always see Santa Claus riding a shark.

Thank God it’s not the Pope.

I see a shark riding the popemobile.

We almost have enough characters for the cast of The Last Supper. Too bad the comments have run out.

That’s it then. The shark jumped the primate.

I see Optimus PRIME! (sad trombone sound)

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.

Shooped. Can tell by the pixels.

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

I saw Math Jesus.

Wow! It’s a schooner!

It’s a SCHOONER!

Now that you mention it, I’m getting a LOT of texture there, fluctuating between Hindu and Mayan, very elegant.

What other ways can it/has it been visualised?

One girl saw the virgin mary’s toast.

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.

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

And there will be a prime number of 1s. Why? Because it’s 2^p-1.

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.

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…

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.

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

(They can

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

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

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

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://www.youtube.com/watch?v=4J9MRYJz9-4

Ooooo, computerized toast! I’m in!

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.)

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

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

http://i50.tinypic.com/2ahbdk4.jpg

Dad?

That’s exactly how I thought it should look!