4 ms·

I think the more interesting way to do this would be to create a border that's roughly circular to frame the giraffe, and fill that border with noise. Then do

I think the more interesting way to do this would be to create a border that's roughly circular to frame the giraffe, and fill that border with noise. Then do the incrementing thing, and your 12 or so bits of noise at the end will blend in better, making it harder for the average person to reverse engineer. I'm imaging something like this, but with a giraffe instead: https://6d4be195623157e28848-7697ece4918e0a73861de0eb37d08968.ssl.cf1.rackcdn.com/873_200w.jpg https://6d4be195623157e28848-7697ece4918e0a73861de0eb37d0896... (Sorry for unreadable CDN link)

mkl 9y ago
I had the same sort of idea, and just implemented it in Python using gmpy2 for the primality check. Here's a prime smiley face: 111010101111001000110101111111001001000010000 000000000000000000000000000000000000000000001 000000000000000001110111111100000000000000001 100000000000011110000000000011010000000000001 000000000011100000000000000000011100000000000 100000000100000000000000000000000011000000001 100000011000000000000000000000000000100000001 100000110000000001000000001000000000011000001 100000100000000001000000001000000000001100000 000001000000000001000000001000000000000100001 100010000000000001000000001000000000000010000 000010000000000001000000001000000000000010001 000010000000000001000000001000000000000010000 000010000000000000000000000000000000000010000 100010000001100000000000000000001100000010001 000001000000110000000000000000011000000100000 000000100000011000000000000000110000001100001 100000110000001111000000000111100000011000000 000000011000000001111111111100000000100000000 100000000100000000000000000000000011000000001 000000000011100000000000000000011100000000000 100000000000011110000000000011010000000000000 100000000000000001110111111100000000000000000 100000000000000000000000000000000000000000001 111011110010001011101100010110111111110011001 As a number, it's 418286130038247526051590581692998429049634527936177232676862400134230223310124567196900044669909574838414882468188159808593146618824409867113710174334769625185535031892647808338085451521099179358299885075661065903947563499117521951858387121272237585876050870984471996640946451287415573046990997289875221396633775785411121263373993999302553. This took 487 random border attempts to find, which seems pretty small! Note that efficient primality tests are probabilistic, so there's a small chance this isn't actually prime. I expect it's the same with the giraffe one in the link. Edit: Here's the code (improved a bit over what made the picture above): https://gitlab.com/snippets/1694391 https://gitlab.com/snippets/1694391
- Smaug123 9y ago
  It is provably prime; I got Mathematica to generate a certificate for it in about five minutes using `PrimeQCertificate`.
  - phkahler 9y ago
    Sometimes its a good idea to use a faster probable prime test when searching, and then use a slower test to verify the result. As has been done here.
    - SAI_Peregrinus 9y ago
      Lenstra and Pomerace's variant of the AKS test is O(log(n)^6), and deterministic. So polynomial, and not a huge exponent. Still not as fast as the probabilistic algorithms, but not as slow as pre-AKS methods.
      - YomiK 9y ago
        "not as slow as pre-AKS methods." only in terms of provable asymptotic bounds. It's much slower than APR-CL and ECPP, both of which existed before AKS, and are the methods used daily.
- jdnier 9y ago
  Playing with the wrap width (in this case 94), you'll see a small herd of giraffes instead. (This is the prime from the reddit article, rather than your smiley face. Easier to see white on black.) 100000000000000000000000000000000000000000000000000000000000000110000000000000000000000000000000 000000000000000000000000000000111000000000000000000000000000000000000000000000000000000000000111 110000000000000000000000000000000000000000000000000000000000111111000000000000000000000000000000 000000000000000000000000000011111110000000000000000000000000000000000000000000000000000000011111 111000000000000000000000000000000000000000000000000000000001000011110000000000000000000000000000 000000000000000000000000000000000111000000000000000000000000000000000000000000000000000000000000 011110000000000000000000000000000000000000000000000000000000000000111100000000000000000000000000 000000000000000000000000000000000011110000000000000000000000000000000000000000000000000000000000 000111100000000000000000000000000000000000000000000000000000000000011111000000000000000000000000 000000000000000000000000000000000000111110000000000000000000000000000000000000000000000000000000 000011111100000000000000000000000000000000000000000000000000000000000111111100000000000000000000 000000000000000000000000000000000000011111111100000000000000000000000000000000000000000000000000 000000111111111100000000000000000000000000000000000000000000000000000011111111111000000000000000 000000000000000000000000000000000000000111111111111000000000000000000000000000000000000000000000 000000001111111111111100000000000000000000000000000000000000000000000000111111111111111100000000 000000000000000000000000000000000000000011111111111111111000000000000000000000000000000000000000 000000001111111111111111110000000000000000000000000000000000000000000000111111111111111111000000 000000000000000000000000000000000000000011111111111111111110000000000000000000000000000000000000 000000001111111111111111111000000000000000000000000000000000000000000000011111111111111111100000 000000000000000000000000000000000000000001111111111111111110000000000000000000000000000000000000 000000000111100001111111110000000000000000000000000000000000000000000000011110000011111111000000 000000000000000000000000000000000000000001111000000111111100000000000000000000000000000000000000 000000001111100000011111110000000000000000000000000000000000000000000000110110000000110111000000 000000000000000000000000000000000000000011011000000011101110000000000000000000000000000000000000 000000011001100000001110111000000000000000000000000000000000000000000001100110000000111001110000 000000000000000000000000000000000000000110011000000011100110000000000000000000000000000000000000 000000011001100000001100011000000000000000000000000000000000000000000000110010000000100001100000 000000000000000000000000000000000000000001001000000110000110000000000000000000000000000000000000 000000000011100000010000011000000000000000000000000000000000000000000000001110000011000001100000 000000000000000000000000000000000000000000011000011000000110000000000000000000000000000000000000 000000000001100001100000011000000000000000000000000000000000000000000000000111001100000001100000 000000000000000000000000000000000000000000011100110000000110000000000000000000000000000000000000 000000000001010011000000010000000000000000000000000000000000000000000000001100000000000011000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001000101101001

mkl 9y ago

I had the same sort of idea, and just implemented it in Python using gmpy2 for the primality check. Here's a prime smiley face: 111010101111001000110101111111001001000010000 000000000000000000000000000000000000000000001 000000000000000001110111111100000000000000001 100000000000011110000000000011010000000000001 000000000011100000000000000000011100000000000 100000000100000000000000000000000011000000001 100000011000000000000000000000000000100000001 100000110000000001000000001000000000011000001 100000100000000001000000001000000000001100000 000001000000000001000000001000000000000100001 100010000000000001000000001000000000000010000 000010000000000001000000001000000000000010001 000010000000000001000000001000000000000010000 000010000000000000000000000000000000000010000 100010000001100000000000000000001100000010001 000001000000110000000000000000011000000100000 000000100000011000000000000000110000001100001 100000110000001111000000000111100000011000000 000000011000000001111111111100000000100000000 100000000100000000000000000000000011000000001 000000000011100000000000000000011100000000000 100000000000011110000000000011010000000000000 100000000000000001110111111100000000000000000 100000000000000000000000000000000000000000001 111011110010001011101100010110111111110011001 As a number, it's 418286130038247526051590581692998429049634527936177232676862400134230223310124567196900044669909574838414882468188159808593146618824409867113710174334769625185535031892647808338085451521099179358299885075661065903947563499117521951858387121272237585876050870984471996640946451287415573046990997289875221396633775785411121263373993999302553. This took 487 random border attempts to find, which seems pretty small! Note that efficient primality tests are probabilistic, so there's a small chance this isn't actually prime. I expect it's the same with the giraffe one in the link. Edit: Here's the code (improved a bit over what made the picture above): https://gitlab.com/snippets/1694391 https://gitlab.com/snippets/1694391

Smaug123 9y ago
It is provably prime; I got Mathematica to generate a certificate for it in about five minutes using `PrimeQCertificate`.
- phkahler 9y ago
  Sometimes its a good idea to use a faster probable prime test when searching, and then use a slower test to verify the result. As has been done here.
  - SAI_Peregrinus 9y ago
    Lenstra and Pomerace's variant of the AKS test is O(log(n)^6), and deterministic. So polynomial, and not a huge exponent. Still not as fast as the probabilistic algorithms, but not as slow as pre-AKS methods.
    - YomiK 9y ago
      "not as slow as pre-AKS methods." only in terms of provable asymptotic bounds. It's much slower than APR-CL and ECPP, both of which existed before AKS, and are the methods used daily.
jdnier 9y ago
Playing with the wrap width (in this case 94), you'll see a small herd of giraffes instead. (This is the prime from the reddit article, rather than your smiley face. Easier to see white on black.) 100000000000000000000000000000000000000000000000000000000000000110000000000000000000000000000000 000000000000000000000000000000111000000000000000000000000000000000000000000000000000000000000111 110000000000000000000000000000000000000000000000000000000000111111000000000000000000000000000000 000000000000000000000000000011111110000000000000000000000000000000000000000000000000000000011111 111000000000000000000000000000000000000000000000000000000001000011110000000000000000000000000000 000000000000000000000000000000000111000000000000000000000000000000000000000000000000000000000000 011110000000000000000000000000000000000000000000000000000000000000111100000000000000000000000000 000000000000000000000000000000000011110000000000000000000000000000000000000000000000000000000000 000111100000000000000000000000000000000000000000000000000000000000011111000000000000000000000000 000000000000000000000000000000000000111110000000000000000000000000000000000000000000000000000000 000011111100000000000000000000000000000000000000000000000000000000000111111100000000000000000000 000000000000000000000000000000000000011111111100000000000000000000000000000000000000000000000000 000000111111111100000000000000000000000000000000000000000000000000000011111111111000000000000000 000000000000000000000000000000000000000111111111111000000000000000000000000000000000000000000000 000000001111111111111100000000000000000000000000000000000000000000000000111111111111111100000000 000000000000000000000000000000000000000011111111111111111000000000000000000000000000000000000000 000000001111111111111111110000000000000000000000000000000000000000000000111111111111111111000000 000000000000000000000000000000000000000011111111111111111110000000000000000000000000000000000000 000000001111111111111111111000000000000000000000000000000000000000000000011111111111111111100000 000000000000000000000000000000000000000001111111111111111110000000000000000000000000000000000000 000000000111100001111111110000000000000000000000000000000000000000000000011110000011111111000000 000000000000000000000000000000000000000001111000000111111100000000000000000000000000000000000000 000000001111100000011111110000000000000000000000000000000000000000000000110110000000110111000000 000000000000000000000000000000000000000011011000000011101110000000000000000000000000000000000000 000000011001100000001110111000000000000000000000000000000000000000000001100110000000111001110000 000000000000000000000000000000000000000110011000000011100110000000000000000000000000000000000000 000000011001100000001100011000000000000000000000000000000000000000000000110010000000100001100000 000000000000000000000000000000000000000001001000000110000110000000000000000000000000000000000000 000000000011100000010000011000000000000000000000000000000000000000000000001110000011000001100000 000000000000000000000000000000000000000000011000011000000110000000000000000000000000000000000000 000000000001100001100000011000000000000000000000000000000000000000000000000111001100000001100000 000000000000000000000000000000000000000000011100110000000110000000000000000000000000000000000000 000000000001010011000000010000000000000000000000000000000000000000000000001100000000000011000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000001000101101001