[goldenkey]

I'm just going to link to this post: http://math.stackexchange.com/questions/311610/modified-eule...

Primes have a pattern, just obvious by their definition. They are self-similar. That doesn't mean there will be some magic non-linear formula for generating primes or detecting primality. But it does mean there are properties that might not be so obvious.

[Someone]

"That doesn't mean there will be some magic non-linear formula for generating primes"

That is correct, but there are magic non-linear formulas for generating only negative numbers and primes. See https://en.m.wikipedia.org/wiki/Formula_for_primes#Formula_b... or http://mathworld.wolfram.com/Prime-GeneratingPolynomial.html

There also is a very simple function that only produces primes, but not all of them: https://en.m.wikipedia.org/wiki/Formula_for_primes#Mills.27_..., https://en.m.wikipedia.org/wiki/Mills%27_constant

[goldenkey]

Thanks for the links. Very interesting stuff. I am definitely going to keep these bookmarked. Mill's constant can be a bit like cheating if it is irrational, because that would mean it is equivalent to packing all the primes into a decimal expansion. But that's just what I read off the surface, I have to see why it's in the form that it is. Just saying, from an information theoretic approach.