Goldbach's Conjecture, Pattern Recurrence, and Fractal SymmetryIn our last study we talked about masking patterns in Goldbach pairs. In this study we focus on the recurrence of those patterns between numbers. We also notice that the patterns recur at different scales of focus. This suggests that prime distribution has fractal symmetry of scale. 
Written November 2008 Last Modified January 2010 (language improvements and links) 

Part 1: Pattern RecurrenceFor any number, there exists a set of other numbers that have the same masking pattern for the same set of critical primes. This is pattern recurrence D1 RecurrentsThe obvious masking pattern recurrence occurs when different numbers share exactly the same sequence of factors for a given set of critical primes. These we will call the D1 Recurrents.
Recall, this is for numbers smaller than 11^2=121. 
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Part 2: Symmetry of Scale: D2, D4, D8 RecurrentsWe may change our scale of view by 2^n. Each zoom will produce new numbers with the same masking pattern. We may also change our scale by any other number, but this requires us to ignore the factors of that number.



Thus for one number to be an exception many others, probably too many others, would also have to be exceptions. Goldbach's Conjecture would then have to be true. Note: the recurrent masks also carry very strong implications about where primes have to occur on the number line. That is, by using recurrent masks we can show where primes must pair up to produce a prime pair in the recurrent mask. 

Part 3: Proving or Disproving Goldbach with Pattern Recurrence and Symmetry of Scale To Prove:
To Disprove
