Primify

This program can convert an arbitrary image into a prime. Given an image, it will generate a base-ten number with the same amount of digits as the image has pixels with 9 representing black and 0 representing white. This can be converted back into a greyscale image.

Usage

1. Open primify.nb with Mathematica
2. Replace the placeholder picture of a computer with your desired image (copy-paste or drag-and-drop). See Image Considerations for optimal formatting.
3. Run the preprocessing cells.
4. Run the Parallel Search cell. Eventually, this will output a number. When it does, abort the cell (Evaluation -> Abort Evaluation).
5. Copy this number into the myPrime = cell.
6. Run the following cells to ensure your image is indeed a prime, and to see how it looks.

The search takes about 20-30 minutes for a 109x109 pixel image on my i7-12650H.

Image Considerations

• Your image will be converted into grayscale image
• It is recommended that the dimensions of your image be SomePrime x SomePossiblyDifferentPrime. This way, when converting your number into an array of pixels, there is only one reasonable way to do so. Of course, this is purely stylistic; the program will work irrespective of which dimensions are chosen.
• The author has specifically tested 109x109 and 131x97 images. The program generated a prime in approximately 20-40 minutes.

Examples

Gets converted into

With the corresponding prime:

91101111111111111111111111111111111110011110111110111110111011011100111111101111110111111111111111111111111101111111101100111111111111111111111110111111111111011111111110110111111011111111111110111111111111111111111111111011111111111001011111111111111111110111111110111011111110111111011110101011111110111111111111111111111111111111111110111111111111111111111111111011111111111111111111111111110111111111111100111111111111111111111111111111111111111010111011111111111111111011111111111101111011110110111111111111111111101111111111111111111111111111111111001111111111110111111111111111111111111111111111111111111111111101111111110111101011111111111111101111111111111111111111111111111111111111111111111111111011111111111111111111110111111101111111111111101111011111111111111111111111111111111111111111111101111111111111111111111111011111111111111111101111111111111111111011111111111111111111111111011111111111111111111111111111111111110111111101111111111111111111111111111111101111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111110111111111011111111111111111111111111111111111111111111111111111111111111111011111111111111110111111111111111111111111111111111111111111111111111111111111111111101011111111111111111111111111111111111111101111111111111111111111111111111111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111011111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111101111011110122212221121222222222222322222233233223333333333334333334333444444444444444311111111111111111111111111111111478888888888888898888888888888888888888888888888888888888888888888888888888776111101111111011011111111111111378787888888888888887888888888888787888878888888888888888888888888888988888888721111111111111111111111111111148888888878888888888878888888888888888888888888888888888888888888888888888888882111111111111111111111111111114888888887888888888888888888888888888888888888888888888888888888888888888888888211111111111111111111111111111478878888888888888888888888888888888888888888888888888888888888888888888888888821111111111111111111111111111137888888888888888888888888888888888888888888888888888888888888888888888888888782111111111111111111111111111114788888888888888888888888888888888888888888888888888888888988888888888888888887211111111111110111111111111111478888888888888888888888888888888888888888888888888888888888888888888888888888821111111111111111111111111111148788888888888888888888888888888888888888888888888888888888888888888888888888882111111111111111111111111111114788888888888888888888888888888888888888888888888888888888888888888888888888887211111111111111111111111110111478888788888888888888888888888888888888888888888888888888888888888888888888888821111111111111111111111111111148888888888888888888888888888888888888888888888888888888888888888888888888888883111111111111111111111111111114888888888888888888888888888888888888888888888888888888888888888888888888888887311111111111111111111111111111488888888888888888888888888888888888888888888888888888888888888888887888888888831111111110111111111111111111158888888888888888888888888888888888888888888888888888888888888888888888888888783111111111111111111111111111115888888888888888888888888888888888888888888888888888888888888888888888888888878311111111111111111111111111111588888888888888888888888888888888888888888888888888888888888888888888888888887831111111111111111121111111111158888888888888888888888888888888888888888888888888888888888888888888888888888873111111111111111111111111111115788888888888888888888888888888888888888888888888878888888888888888888888888877411111111111111111111111111111588888888888888888888888888888888888888888888888888888888888888888888888888878741111111111111111111111111111168888888888888888888888888888888888888888888888888888888888888888888888888888884111111111111111111111111111115888888888888888888888888888888888888888888888888888888888888888888888888888878411111111111111111112111111111688888888888888888888888888888888888888888888888888888888888888888888888888888741111111111111111112222111111158888888878888888888888888888888888888888888888888888888888888888888888888888874111111111111111111222112111116888888888888888888888888888888888888888888888888888888888888888888888888888888511111111111111111222221111111588888888888888888888888888888888888888888788888888888888888888888888888888888751111111111111111122212111211168888888888888888888888888888888888888888888888888888888888888888888888888888785111111111111111112222221122116878888888888888888888888888888888888888888888888888888888888888888888888888888511111111111111111222221111111688888888888888888888888888888888888888888888888888888888888888888888888888887851111111111111111122221121111268888888878888888888888888888888888888888888888888888898888888888888888888888885111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