New and revolutionary data comression scheme!

Infinite compression?

I've always was interested in how compressed files worked and why the compression factor is so low.
The entropy explanation isn't something i would accept without tinkering with the data. The idea of my compression algorithm(currently under development) is to
use algebraic properties of files to express the data in more concise way.
The thing might sound trivial, but its implementation is not.
Normal compression works by splitting FILE and finding redundant pieces to express them in minimum volume.
Imagine a FILE read and converted to arbitrary precision integer. Now consider all the myriad ways to generate said integer. Sounds difficult? Not so much.
1.lets take a Prime Number,e.g. 2 and raise it to power closest to our integer, e.g. 20000. Note the difference from the (FILE-result).
2.Get the smallest difference with the powers available,
and proceed to next step:
3.If the difference is negative: find 2 raised to the power
of X which would close the gap,by substracting it from #1
If the difference is positive just add 2 with closest power to the difference .
The end result could be something like
2^6+2^5-2^3+2^1-2^0=Integer=FILE
Its can be improved further by using other prime numbers powers with the idea of expression taking the least space.
The same thing can be accomplished with arbitrary length floating point numbers like 2^123712.1282 which would converge faster,but will require some fixing to convert to a stable binary result.
Posted by FrozenVoid at 15:37

I'm off to watch some anime so here the draft pseudocode for compression:

1.build array of 100(or 10000 whatever) primes from sequence of primes
2.get a file e.g. http://marknelson.us/attachments/million-digit-challenge/AMillionRandomDigits.bin
(the above is statistically random binary noise)
3.convert the file into INTEGER
4. for(i=0;i<ArrayOfPrimes;i++){
ArrayOfPrimes[i]^DoubleFloatPowerY =Z->convert to Integer->compare to 3.
//find the prime number & power which is closest,(in terms of absolute value,not larger or smaller) than 3.INTEGER
 }
5.calculate the difference between 4. and 3. this number is new INTEGER
6.apply process from 4. to this INTEGER, until the result is :
3.INTEGER=x^y-z^n+k^v. etc
(in other versions this can be used with multiplier/divisors picked instead of 5.)



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