Just so I don't wait any longer to put this out there:
I had a fascinating idea about the Primes the other day. Looking at the number line, and skipping one to make things come out, we start with two as the first prime number and knock off every even number. On a line, this is a wave with period 2.
Now the next number not on a wave is 3, which is the next prime and starts a wave with period 3. 4's out, so 5 is the next prime with period 5.
The first thing I noticed was that the number of waveforms involved grow very large very quickly. The next thing I noticed was the seeds of a possible chaotic/indeterminate angle in that.
But then I got to thinking. If you could find some way to analyze the waves in the aggregate you could solve for the next prime. If you could prove that their is no way to analyze the waves in the aggregate, you'd be off to a good start that prime number prediction is simply too complex to solve with standard math.
I get the feeling I'm probably not blazing too much of a trail on this, but it is nice to see it in print.
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