I had an idea awhile back about treating large files as insanely large hex integers, then dividing that by a huge known prime, and basically storing 3 smaller integers that plug into the equation "ax + b", where x is the known prime, a is what you found when doing the division, and b is the remainder. Plugging those numbers into the equation would give you the huge integer representing the original file. I'm assuming…
One formulation is 2(11)+3. The primes up to 25 are 2,3,5,7,11,13,17,19,23, so we'll use the index 4 to represent the prime number 11.
To lay this out, we need to represent three numbers: 2, 4, and 3. Without the inevitable markings you'd need to delineate when numbers started and stopped, the bit string would look like 10 100 11.
Using 11 as the prime, your compression would require laying out 1010011 to represent 11001, which means it's actually anti-compression.