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Images Created from Prime Numbers

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Re: Images Created from Prime Numbers

#51

Post by cygaril »

oefrha wrote: post #34
war1025 wrote: post #28

Semi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word. Basically, prime numbers that differ by exactly one binary digit in their representation. Probably nothing about that relationship that would be interesting enough to look into beyond just "I ran some calculations and found these numbers that fit the pattern"

This is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a. http://michaelnielsen.org/polymath1/index.php?title=Bounded_... Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.

I think you were right the first time.

Re: Images Created from Prime Numbers

#52

Post by cygaril »

mc3 wrote: post #39
kvakil wrote: post #26

Earlier quoted context omitted.

In addition, even if a normal number was used, it's far simpler to describe the data by just using a single number alone. For example, a binary encoding of the data (perhaps using a prefix-free code). Using a normal number and two "positions" is just more complicated.

Nonetheless, it's freaky that our deepest secrets are encoded into pi. If pi is normal.

https://maskofreason.files.wordpress.com/2011/02/the-library...

Re: Images Created from Prime Numbers

#54

Post by goldenkey »

lonelappde wrote: post #21
ardit33 wrote: post #11

Earlier quoted context omitted.

you can encode any arbitrary information into a one dimensional value.... eg: a large enough number can encode the whole universe.... But decoding any meaningful information has to be at least in two dimensions.... In two dimensions, you can describe everything.... the other dimensions are not needed (and perhaps just emerging, according to the holographic principle)....

> But decoding any meaningful information has to be at least in two dimensions.... What does this mean?

It's the uncertainty principle and principle of orthogonal observables. Energy vs time for example. You need two dimensions for a comparison. One dimension is static.

Re: Images Created from Prime Numbers

#55

Post by goldenkey »

extr wrote: post #9

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.

Dimensions can always be compressed and uncompressed.

Naturals: https://en.wikipedia.org/wiki/Pairing_function

Reals: https://en.wikipedia.org/wiki/Space-filling_curve

The caveat is that a function, like the evolution of the universe, General Relativity, differential equations, would be possibly unwieldy and unaesthetic when written on lower dimensions, and locality might also be lost.

Some techniques try to preserve locality:

https://en.wikipedia.org/wiki/Z-order_curve

The takeaway is that any object, nomatter how complex, can be represented as a single number. That is the basis of Godel Numbering: https://en.m.wikipedia.org/wiki/G%C3%B6del_numbering

Re: Images Created from Prime Numbers

#56

Post by oefrha »

cygaril wrote: post #51
oefrha wrote: post #34

Earlier quoted context omitted.

This is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a. http://michaelnielsen.org/polymath1/index.php?title=Bounded_... Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.

I think you were right the first time.

Nah, 3 (0b11) and 5 (0b101) differ by 2^1 but differ by two binary digits. Or 7 (0b111) and 11 (0b1011). But as I said it’s a starting point.

Re: Images Created from Prime Numbers

#57

Post by twic »

ConcernedCoder wrote: post #41
ShorsHammer wrote: post #14

Earlier quoted context omitted.

The entire Library of Babel is encoded in Pi. https://en.wikipedia.org/wiki/The_Library_of_Babel

So cool, you can find anything you search for: https://libraryofbabel.info/bookmark.cgi?concernedcoder0001 about 1/2 way down the page you can find: "concerned coder is a programmer living in the sourthern usa, playing a game called eve online while reading hacker news on a sunday night in january"

Hmm. Other sources suggest that Concerned Coder is a programmer living in the northern USA, playing a game called Eve Online while reading Hacker News on a Sunday night in January:

https://libraryofbabel.info/bookmark.cgi?concernedcoder00001...

Re: Images Created from Prime Numbers

#58

Post by danwills »

kijin wrote: post #5
uyaij wrote: post #2

Explanation from an article referenced by the linked article[1]: Most of the digits were fixed while the rest could be brute-forced using some useful properties. [1] https://www.futilitycloset.com/2017/09/10/trinity-hall-prime...

From the link: > approximately one in every 6200 2688-digit numbers is prime. So if you're lucky, you only need to brute force the last 4 digits! Maybe 5 if you're unlucky. In either case, that's a lot less work than I imagined. And of course you can skip all the even numbers.

Kinda more 'primes from images' (w/a tiny area that can't be used) than 'images from primes'. Still cool though!

Re: Images Created from Prime Numbers

#59

Post by cyborgx7 »

lonelappde wrote: post #19
nayuki wrote: post #4

Reminds me of this classic number: https://en.wikipedia.org/wiki/Illegal_prime Basically: DeCSS source code (illegal) → compress → pad → add constant to make it prime.

That article talks about specious attempt to hack the legal system, by claiming information can never be legally restricted because it can encode numbers, but doesn't say the result of the attempt.

Copyright does make numbers illegal. I think it is less about "hacking" the legal system, and more about demonstrating how nonsensical it is.

Re: Images Created from Prime Numbers

#60

Post by askvictor »

JKCalhoun wrote: post #44
egypturnash wrote: post #33

Mostly unrelated but this made me check to see if the Prime Number Shitting Bear is still online. It is! https://alpha61.com/primenumbershittingbear/

The classic prime joke (saw it originally in Sci Am back in the ... 70's? 80's?). Found an approximation when I googled it: A mathematician, physicist, and engineer are taking a math test. One question asks "Are all odd numbers prime?" The mathematician thinks, "3 is prime, 5 is prime, 7 is prime, 9 is not prime -- nope, not all odd numbers are prime." The physicist thinks, "3 is prime, 5 is prime, 7 is prime, 9 ...…

The version I remember has the mathematician thinking: "3 is prime, 5 is prime, 7 is prime, so by mathematical induction, all odd numbers are prime".
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