The Bilateral 9 Sums

Root 4x
29
 └── 30
      └── 31
           └── 32
    
Rewrite Root 4x → Twin 4x

Root 4x
29
 └── 30
      └── 31
           └── 32
    
Twin 4x
33
 └── 34
      └── 35
           └── 36

  -----------------------+----+----+----+----+
   True Prime Pairs Δ    |  1 |  2 |  3 |  4 | 
  =======================+====+====+====+====+
   19 → π(10)            |  2 |  3 |  5 |  7 | 4 x Root
  -----------------------+----+----+----+----+
   17 → π(20)            | 11 | 13 | 17 | 19 | 4 x Twin
  -----------------------+----+----+----+----+
   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - | ← Rewrite here
  =======================+====+====+====+====+
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  -----------------------+----+----+----+----+----+----+----+----+----+-----
   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
  =======================+====+====+====+====+====+====+====+====+====+=====
   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
  -----------------------+----+----+----+----+----+----+----+----+----+-----
   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
  -----------------------+----+----+----+----+----+----+----+----+----+-----
   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ←------------ Rewrite here
  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin

Recombimation

default

  -----------------------+----+----+----+----+----+----+----+----+----+-----
   True Prime Pairs Δ    |  1 |  2 |  3 |  4 |  5 |  6 |  7 |  8 |  9 | Sum 
  =======================+====+====+====+====+====+====+====+====+====+=====
   19 → π(10)            |  2 |  3 |  5 |  7 |  - |  - |  - |  - |  - | 4th  4 x Root
  -----------------------+----+----+----+----+----+----+----+----+----+-----
   17 → π(20)            | 11 | 13 | 17 | 19 |  - |  - |  - |  - |  - | 8th  4 x Twin
  -----------------------+----+----+----+----+----+----+----+----+----+-----
   13 → π(30) → 12 (Δ1)  | 23 | 29 |  - |  - |  - |  - |  - |  - |  - |10th ←------------ 10
  =======================+====+====+====+====+====+====+====+====+====+===== 1st Twin
   11 → π(42)            | 31 | 37 | 41 |  - |  - |  - |  - |  - |  - |13th
  -----------------------+----+----+----+----+----+----+----+----+----+----- 2nd Twin
    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th
  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
  =======================+====+====+====+====+====+====+====+====+====+=====  ←-- Rewrite here (bilateral 9 sums)
    3,2 → 18+13+12 → 43  | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th ------------→ 30
  =======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
    5 → π(72) → 18 (Δ13) | 61 | 67 | 71 |  - |  - |  - |  - |  - |  - |20th ←------------ 20
  -----------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
    7 → π(60) → 19 (Δ12) | 43 | 47 | 53 | 59 |  - |  - |  - |  - |  - |17th