You know, in theory, you could encode any binary data as its nearest prime number, plus or minus a delta number, which would be an integer...
And... check this out... the delta number itself -- might be in turn composed of one or more prime numbers, plus or minus a smaller delta -- until the delta no longer can be expressed as containing another prime number inside of itself!
Which leads to an interesting question... are prime gaps, that is, the space between prime numbers,
are prime gaps fractal in nature?
In other words, what's the mathematical relationship between say filling up a prime gap (and I'm thinking as those gaps become larger and larger, as the prime numbers themselves become larger and larger) with one or more smaller primes, plus a delta (the delta being the point where you run out of primes for covering the gap, that when added or subtracted, brings you back to your original binary data, expressed as a large integer, or the closest largest prime...)
Well, what's the exact relationship there, and can it be used for (one of my favorite topics! <g>), data compression?
?
(Yes, this set of ideas needs some tweaking and/or more formal definition... this is the "rough draft" of that future formal definition...)
