Are those some new symmetries among the Twin Primes?

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For each pair of Twin Primes $(p_a;p_b)$, the following operation gets applyed:

  1. Concatenation of the pair to one real number $R_{ab}$ by using a comma inbetween for separation.
  2. Calculating the square of that real number.
  3. Decouple the squared real number at the comma back into two integers again.
  4. Calculating the sum $S_{ab}$ of those two integers.

Example:

$(p_a;p_b)=(59;61)$

  1. $R_{ab}=59,61=61,59.$
  2. $R_{ab}^2=(59,61)^2 = 3553,3521$ and $R_{ba}^2=(61,59)^2=3793,3281.$
  3. $S_{ab}=3553+3521= 7074 = 3793+3281 = 7074 = S_{ba}. $

I'm looking for any explanation on some results of this operation like below:

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