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My theory

  1. take a file examplesize:(3GB)

  2. convert said file to a number

  3. divide that number by a large prime number example:(2^82,589,932 · (2^82,589,933-1))[2018 Dec 07]

  4. get the quotient and the remainder

  5. if the remainder is still large do the math again to get another quotient and remainder until the remainder size is as small as preferred

  6. build the compressed data

    FFFF - First division
EEEE - Second division
....
LLLL - Final remainder length(hex)
RRRR - Final remainder
ZZZZ - File Name   
Example: 0000ABC60000EF53....000468438FB1412e62696e
Example: FFFFFFFFEEEEEEEE....LLLLRRRRRRRRZZZZZZZZZZ

Because there are only 51 confirmed primes larger then 2 (as of 2018 Dec 07) and we would only need the longest 20 primes to shrink a file to the max useful size we would only need 80 bytes plus the remainder and file name.

For a (by my calculations)108PB file this could bring the file size to a few Kilobytes in size at most

Does this even sound feasible

Steven
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    The algorithm is unclear and should be explained formally. Anyway, what you say cannot be true. There are $2^{108 \cdot 2^{53}}$ files of size 108PB, so any lossless compression scheme must use at least $\log 2^{108 \cdot 2^{53}} = 108 \cdot 2^{53}$ bits on at least one of these files... i.e., $108$ PB. Besides, what do you mean by "there are only 51 confirmed primes larger than 2" ??? – Steven Apr 01 '21 at 21:27
  • the only confirmed primes above 2 are listed here https://www.mersenne.org/primes/ and – Steven Apr 01 '21 at 21:31
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    You are talking about Mersenne prime numbers, not arbitrary Prime numbers. Anyway, I totally with the first comment. –  Apr 01 '21 at 21:33
  • These are Mersenne primes. It is a well-known fact that there are infinitely many prime numbers (if not, then suppose towards a contradiction that the $n \ge 2$ primes are $p_1, \dots, p_n$. Then $p^* = p_1 \cdot p_2 \cdot \ldots \cdot p_n + 1$ has remainder $1$ when it is divided by any $p_i$, therefore $p^$ must be prime. This is a contradiction since $p^$ is larger than any $p_i$). – Steven Apr 01 '21 at 21:35
  • i know there are infinitely many prime numbers but im trying to use large static numbers(so the devisor does not have to be shared with the file) to divide into numbers from data files to get both a smaller number and get the remainder and to get the 108PB size was by taking the file size of (2^82,589,932 · (2^82,589,933-1))[25MB] * 4,294,967,295 (FFFF FFFF) this does not include the other 19 that could be used so it is probably larger – Steven Apr 01 '21 at 21:59
  • The only issue i am currently stuck on is how as i supost to load the file and perform a division when i cant get any coding language to load more then a 2GB file in to memory. also the reason im using primes to do this is because they are constants – Steven Apr 01 '21 at 22:03
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    I suggest reading https://cs.stackexchange.com/q/7531/755 and https://en.wikipedia.org/wiki/Lossless_compression#Limitations and https://cs.stackexchange.com/q/50052/755. You seem to be doing the equivalent of trying to invent a perpetual motion device, which is of course impossible and thus it's hardly worth getting into the details when we already know that what you're trying to do ain't gonna work. – D.W. Apr 01 '21 at 22:06
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    Does this answer your question? No compression algorithm can compress all input messages? – Yuval Filmus Apr 02 '21 at 07:06

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