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 2007-11-01, 04:11 #1 jasong     "Jason Goatcher" Mar 2005 5×701 Posts Picture primes I'd like to learn how to find picture primes, and in the process, help others to accomplish this. For those of you who don't know, a picture prime is a prime number where when it is displayed at a certain number of digits per line, a picture, word, or many words is formed. I will describe what I think is the best method for doing this and hope that people can help me find programs that can accomplish each task. First, we need to know the picture or sentence we want. For this we'll use "PRIME NUMBERS ARE SUPER-COOL!!!" Cheesy, but then again, a lot of people think prime number searching as a hobby is cheesy. Next, one needs to find a program that can represent the bit-map of that sentence. Another problem is how big a square to use for each pixel, a square that will be represented by digits. And will the "pixels" all be one digit with another digit representing white space? What if one decides they want to list a lot of peoples names as prime pictures and the combination of the white space digit and the dark pixels digit is the person's age? Lot's of choices in the particulars. Anyway, if we've got the bit-map and it's saved as a file, then we need a program that can take as input the bit-map, the size of the grid, and possibly the places in the picture that can be any number, since the odds are against our picture being prime right off the bat. After that, it's a matter of sieving a range of numbers, the size of the range being decided by the size of the number. Then you should have a list of possibilities which you can PRP. If luck is on your side you'll get at least one PRP. At that point, the resulting number may be so big that it would be foolish to try to test it to achieve a 100% certainty that it's prime. The place that I got this idea used a method where they knew for a fact that a 100,000 digit number was prime, but without having the necessary math skills, one can only hope to prove a number under 5,000 digits as absolutely prime, and in reality, the limit is probably much, MUCH less than a 5,000-digit limit. Unless, of course, you're reading this a few years after I actually wrote it. I'm prepared for the possibility that this thread post won't achieve it's intended goal and either stay an orphan, or maybe people will be super-enthusiastic, and many posts later give up on the task. But...fingers crossed. And if anyone wants to help the great unwashed use the super-cool, but mysterious n+/-1 method to generate massive primes, that would be fabulous.
 2007-11-01, 11:15 #2 Xyzzy     "Mike" Aug 2002 5·23·67 Posts We're not sure how your method works, but here is a "picture prime" of M27. Attached Thumbnails
2007-11-01, 12:33   #3
m_f_h

Feb 2007

24·33 Posts

Quote:
 Originally Posted by Xyzzy We're not sure how your method works, but here is a "picture prime" of M27.
It seems your method truncates the data:
it seems to display only the MSB (or LSB ? a matter of interpretation in this context ?)
If you cannot avoid truncation, try another data layout (LittleEndian vs BigEndian...)

2007-11-01, 12:38   #4
m_f_h

Feb 2007

24·33 Posts

Quote:
 Originally Posted by jasong I'd like to learn how to find picture primes, and in the process, help others to accomplish this. For those of you who don't know, a picture prime is a prime number where when it is displayed at a certain number of digits per line, a picture, word, or many words is formed. I will describe what I think is the best method for doing this and hope that people can help me find programs that can accomplish each task.
For a given Mersenne prime there is only one way to arrange the binary digits in a rectangular square, and the outcoming pictures are quite similar for all primes of that kind...

2007-11-01, 14:47   #5
Xyzzy

"Mike"
Aug 2002

5·23·67 Posts

Quote:
 It seems your method truncates the data...
No truncation. The entire prime is in there.

Think like a terrorist. (Seriously!)

 2007-11-01, 15:16 #6 paulunderwood     Sep 2002 Database er0rr 344610 Posts I think Jason is referring to a "primeform e-group" "picture prime". Although a message in encoded in the prime, you can hardly call it encryption "Picture" is probably not the most apt term. It would be nice to have a picture prime of M27 (above.) The possibilities are endless We used some kind of "banner" program -- "man banner" on your Unix/Linux systems. "banner" was used on our continuous stationary at Uni to separate users' print-outs with their account names etc. I will get back to you with the name of the program we used if you cannot find a suitable one with Google. You need an "alphabet" -- a set of letter files -- which are used by the program to turn a message source text input file into the required output. It is an easy task for a budding computer science undergraduate to write such a program. Last fiddled with by paulunderwood on 2007-11-01 at 15:50
 2007-11-01, 15:18 #7 petrw1 1976 Toyota Corona years forever!     "Wayne" Nov 2006 Saskatchewan, Canada 3·52·59 Posts Is this what you are talking about? http://hjem.get2net.dk/jka/math/egroup/picture.htm
 2007-11-01, 15:35 #8 ATH Einyen     Dec 2003 Denmark 3·23·43 Posts I suggest using the gif image format, since you can put arbitrary number of characters as "comments" in a gif-file, so just fill in stuff until your image is prime. check under "Comment Block Extension" http://www.u229.no/stuff/GIFFormat/ Last fiddled with by ATH on 2007-11-01 at 15:35
 2007-11-01, 21:11 #9 jasong     "Jason Goatcher" Mar 2005 350510 Posts While we're on the subject of picture primes, does the fact that the prime was generated using the 15 N-1 factor files(I have no idea of how these were used, so I may be ignorantly referring to something that doesn't matter) disqualify it from the "no special form" category? I'd always thought that that only applied to the final number. Since I'm pretty sure the "no special form" record is significantly less than 100,000 digits, I guess I'm wrong.
 2007-11-01, 22:54 #10 paulunderwood     Sep 2002 Database er0rr 344610 Posts Yes, it has a "special form" because of the 30% factorization of N+1.
2007-11-02, 02:58   #11
Xyzzy

"Mike"
Aug 2002

5·23·67 Posts

Quote:
 Think like a terrorist. (Seriously!)
Code:
$apt-cache show steghide Package: steghide Priority: optional Section: misc Installed-Size: 484 Maintainer: Ola Lundqvist <opal@debian.org> Architecture: i386 Version: 0.5.1-8 Depends: libc6 (>= 2.3.6-6), libgcc1 (>= 1:4.1.0), libjpeg62, libmcrypt4, libmhash2, libstdc++6 (>= 4.1.0), zlib1g (>= 1:1.2.1) Filename: pool/main/s/steghide/steghide_0.5.1-8_i386.deb Size: 174420 MD5sum: 0adc54c1e8783cf5282f0873ea911e5f SHA1: 8556b3f25cbfdaa08dc8a2474b74b05d7cd7e31e SHA256: ba780805044a239b638e8460360c22f3a86c95836ce8ada9d62e84b37c10dceb Description: A steganography hiding tool Steghide is steganography program which hides bits of a data file in some of the least significant bits of another file in such a way that the existence of the data file is not visible and cannot be proven. . Steghide is designed to be portable and configurable and features hiding data in bmp, wav and au files, blowfish encryption, MD5 hashing of passphrases to blowfish keys, and pseudo-random distribution of hidden bits in the container data. Tag: interface::commandline, role::program, scope::utility, security::cryptography, works-with::image, works-with::image:raster$ steghide info gabrielle.jpg
"gabrielle.jpg":
format: jpeg
capacity: 7.3 KB
Try to get information about embedded data ? (y/n) y
Enter passphrase:
embedded file "27.txt":
size: 13.2 KB
encrypted: rijndael-128, cbc
compressed: yes

$steghide extract -sf gabrielle.jpg Enter passphrase: wrote extracted data to "27.txt".$ cat 27.txt
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