Arbirtary Extraction of Primes - From Ideal Fractal(s)?

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7 replies · 2K views
Sinsearach
At a sufficient resolution, such as mapping every knowing prime gap...
Could a fractal equation created to perfectly describe this (at max possible res.):
http://techn.ology.net/the-density-plot-of-the-prime-gaps-is-a-fractal/

Likewise clear a path to a nth-dimensional fractal for prime gaps and then... primes?

Yes I know I'm way out of my depth here, which is why I am asking.
 
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fresh_42 said:
I have no idea what you are talking about. Do you mean this plot here:
https://en.wikipedia.org/wiki/Prime_gap?

ah yes i should have remembered that
now i recall coming across that a few weeks ago
also noticed the easily observed curve plot of maximal gaps as charted 1/4 the way down that WP article
 
... there are infinitely many pairs of prime numbers that differ by 70 million or less ...
This doesn't mean all. There are still gaps of size ##N \in \mathbb{N}## for all ##N##. We don't even know, if there infinitely many pairs of prime numbers that differ by ##2##. There are various upper and lower bounds for the ##n-##th gap.
 
There is a maximal gap for primes smaller than N. There is no absolute maximal gap anywhere.
Sinsearach said:
But note this proof that apparently shows a absolute maximum gap:
It makes a statement about how often small gaps are. It doesn't make any statement about larger gaps.
There is an infinite set of gaps smaller than 70 million and also an infinite set of gaps larger than that.

fresh_42 said:
This doesn't mean all. There are still gaps of size ##N \in \mathbb{N}## for all ##N##.
There is no gap of size 7, for example (unless you count a gap of size 8 as gap of size 7 as well). You probably mean ##\geq N##.