The Reimann Hypothesis

This led to the now-famous Riemann Hypothesis which states simply that all nontrivial zeros of have real part 1/2. This has been confirmed for at least the first 1,500,000,000 zeros, using powerful computers, but this does not constitute a proof!

Not proved, but the approach is to consider the accurate ruler that can measure an integer to the nearest 1/2. Then construct the sample data problem and relate this to the point where fractions and whole number match. The maximum entropy encoding of the ruler would determine the appropriate renormalizing of the ruler, the prime spots, where the sample rate of the ruler can measure the next amount of disorder using the next prime as a quant. Doable, I think, but above my head at the moment. It may be impossible to get a general expression of disorder in the induction.

Unprovable:

 If I know the previous primes, I can derive an expression for the next prime, but that involves me taking the log.  The log is a Taylor series and becomes a numerical method for computing the next prime, with the same number of operations as the next prime will allow.  The proof would be numerically useless and likely unfounded.  The log is really another definition of the prime number line.

So, in other words. You take the product of your previous primes:
1/p2 * 1/p2 * 1/p3... and use that functional to determine the disorder induced. Then show that the next prime, pn, reduces that disorder such that measurements are reduced to less than one half.  You compute the Taylor series about 1, and show that the series reaches the critical point at x = some f(Pn), a function of the next prime.

What have you proven?

Only that the log function works with the prime centered number line, the slide rule works, nothing more.

A better approach:

Show that separable groups induce axii of symmetry called primes, resulting in an  integer line and allow a log function.  Start from group theory.