Our number line likes strong divisibility

Here I have plotted the primes divided by the golden rate taken to the power of the index at the bottom. In other words, primes look increasingly like the golden ratio.  Not much of a clue as we know primes are about divisibility.  The issue is, what is the natural, unseen, curvature of the number line that causes this plot.

Put in other words. There are tiny tick marks along the integer number line that provide granularity allows us to count the elements in disordered groups. At some point there tick marks become inaccurate, and a group becomes uncounted, to the nearest 1/2. When that happens, the number is, by definition, a prime. Primes really are just the definition of a finite number line. The prime number tells us the accuracy up to that point.

The the integer number line, and its fractional tick marks is a composition of hierarchical number lines.  When the number lines, up to a point, can longer distinguish one small item from the next, we pull out the next number line up the scale and make the decision. Works a lot like relativity.

The game we are playing is to try to determine when additional items added to a disordered set do we create a constant uncertainty about the best ordering. When that happens, a significant bit, called a prime ordering, is added to each identical item. The disorder is reduced by one half. Fibonacci is a good, though not complete, measure because it defines the next grouping that is mostly composed of the addition of two largest previous groups.