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

  1. Jul 26, 2017 #1
    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 im asking.
     
  2. jcsd
  3. Jul 26, 2017 #2

    fresh_42

    Staff: Mentor

  4. Jul 26, 2017 #3
    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
     
  5. Jul 26, 2017 #4

    fresh_42

    Staff: Mentor

  6. Jul 26, 2017 #5
  7. Jul 26, 2017 #6

    fresh_42

    Staff: Mentor

    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.
     
  8. Jul 26, 2017 #7

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    There is a maximal gap for primes smaller than N. There is no absolute maximal gap anywhere.
    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.

    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##.
     
  9. Jul 26, 2017 #8

    fresh_42

    Staff: Mentor

    Sure.
     
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