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```
=======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th
=======================+====+====+====+====+====+====+====+====+====+=====
↓
|
↓
114-89=139-114=25=5x5
|
| ----------- 5 -----------
| | |
↓ ↑ ↓
| mapping | feeding | lexering | parsering | syntaxing | grammaring |
|------------- 36' --------------|----------------------------36' ----------------------------|
| 19' | 17' | 13' | 11' | 7' | 5' |
+----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
+----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
| 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |
+----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
↓ ↑ ↓
| | |
------------ 10 ------------- |
|
|
-----------------------+----+----+----+----+----+----+----+----+----+----- |
True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |
=======================+====+====+====+====+====+====+====+====+====+===== ↓
19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)
-----------------------+----+----+----+----+----+----+----+----+----+-----
```

[![default](https://user-images.githubusercontent.com/8466209/199508386-69859804-9ccb-4f5d-8314-8ca0be0af235.png)](https://gist.github.com/eq19/f1af4317b619154719546e615aaa2155#file-pairing-md)

[![default](https://user-images.githubusercontent.com/8466209/199510678-abc4b002-b54a-4a80-9e12-1ef6527ca511.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406#file-mirror-md)
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[![default](https://user-images.githubusercontent.com/8466209/202907205-4c025632-44a7-4cbe-927f-166254803607.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-keyring-md)

[![default](https://user-images.githubusercontent.com/8466209/204159538-6f87b60c-6a32-486d-aa55-c9af2db7eda6.png)
](https://gist.github.com/eq19/f21abd90f8d471390aad23d6ecc90d6d#file-feeding-md)
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```
===========
(1){1}-7: 7’
(1){8}-13: 6‘
(1)14-{19}: 6‘
------------- {6+6} --→ [M+F]
(2)20-24: 5’ |
(2)25-{29}: 5’ |
------------ 5+5 --------
(3)30-36: 7:{70,30,10²} |
------------ |
(4)37-48: 12• --- |
(5)49-59: 11° | |
--}30° 30• |
(6)60-78: 19° | |
(7)79-96: 18• --- |
-------------- |
(8)97-109: 13 |
(9)110-139:{30}=5x6 <--x-- [C1+C2]
--
43
```

```
True Prime Pairs:
(5,7), (11,13), (17,19)
|------------------------ Scheme-12 ------------------------|
|------------ 6¤ -------------|------------- 6¤ ------------|
|--------------------------- 192 ---------------------------|
|---- {23} ----|---- {49} ----|-- {29} -|--{30} --|-- 61 ---|
+----+----+----+----+----+----+----+----+----+----+----+----+
| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 43 |
+----+----+----+----+----+----+----+----+----+----+----+----+
|--------- 5¤ ---------|---- {48} ----|----- {48} ---|{43}|
|--------- 5¤ ---------|------------ {96} -----------|{43}|
|--------- {53} ---------|-------------- {139} -------------|
|------ Scheme-53 -------|------------ Scheme-34 -----------|
```

```
Tabulate Prime by Power of 10
loop(10) = π(10)-π(1) = 4-0 = 4
loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
-----------------------+----+----+----+----+----+----+----+----+----+-----
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
=======================+====+====+====+====+====+====+====+====+====+===== 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
=======================+====+====+====+====+====+====+====+====+====+===== 4th Twin
3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th
=======================+====+====+====+====+====+====+====+====+====+=====
Δ Δ
12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-1
Sequence:
By the next layer the 89² will become 89 and 5 become 5² or 25.
This 89 and 25 are in the same layer with total of 114 or prime 619
So sequence from the first prime is 1,4,7,10,29,68,89,114,139,168,329,618.
```

[![Screenshot](https://user-images.githubusercontent.com/8466209/204251093-ade3969a-ecc5-4f78-9a19-e13439e78e31.png)](https://gist.github.com/eq19/0ce5848f7ad62dc46dedfaa430069857#file-grammar-md)

[![204159170-55a7470a-d03b-49c0-ba3c-68a64f895263](https://user-images.githubusercontent.com/8466209/204254729-71d84d54-b908-4b55-82c2-388cfbd7233c.png)
](https://gist.github.com/eq19/b541275ab7deda356feef32d600e44d8#file-runner-md)

![Screenshot_2022-11-28-16-50-17-00](https://user-images.githubusercontent.com/8466209/204253954-e7dfe758-64a8-442e-8989-67343c9d18ed.png)
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combined. By this 1000 primes then **168-150=Δ18** is raised on the next turn.
```liquid
$True Prime Pairs:
layer | node | sub | i | k | f
------+------+-----+-----+-----+-----
| | | 1 | 1,2 | 2,3 ← 2x = (13-11)x ---
| | 1 +-----+-----+ |
| 1 | | 2 | 3 | 7 |
| |-----+-----+-----+ |
| | | 3 | 4,6 | 10,11,12 -- |
1 +------+ 2 +-----+-----+ | |
| | | 4 | 7 | 13 5x --- |
| +-----+-----+-----+ | | |
| 2 | | 5 | 8,9 | 14,15 ----- | |
| | 3 +-----+-----+ | |
| | | 6 | 10 | 19 | |
------+------+-----+-----+-----+-------- 7x + 6x = 13x
| | | 7 | 11 | 20 | |
| | 4 +-----+-----+ | |
| 3 | | 8 | 12 | 26 ----- | |
| +-----+-----+-----+ | | |
| | | 9 | 13 | 27 2x ----- |
2 +------| 5 +-----+-----+ | |
| | | 10 | 14 | 28 ----- |
| |-----+-----+-----+ |
| 4 | | 11 |15,18| 29,30,31,32 ←---4x----
| | 6 +-----+-----+
| | | 12 | 19 | 36
------+------+-----+-----+-----+-------
| | | 13 | 20 | {38}
| | 7 +-----+-----+
| 5 | | 14 |21,22| {40,41} = (19-17)x ----
| |-----+-----+-----+ |
| | | 15 | 23 | {42} 6x + 13x = 19x
3 +------+ 8 +-----+-----+ |
| | | 16 |24,27| {43,44,45,46} ←- 4x --
| |-----+-----+-----+
| 6 | | 17 | 28 | {50} = 46 + 4
| | 9 +-----+-----+
| | | 18 | 29 | {68} = 32 + 36
------|------|-----+-----+------
```

```liquid
| 1st (Form) | 2nd (Route) | 3rd (Channel) |
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
150 | 151| 152| 153| 154| 155| 156| 157| 158| 159| 160| 161| 162| 163| 164| 165| 166| 167| 168|
=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
Δ1 | 19 | - | 31 | 37 | - | - | - | - | - | - | - | - | - | - | 103| - | - | - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ2 | 20 | 26 | - | 38 | - | - | - | - | - | 74 | - | - | - | 98 | 104| - | - | - |
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ3 | 21 | 27 | - | 39 | - | - | - | - | - | 75 | - | - | - | 99 | 105| - | - | - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ4 | 22 | 28 | - | 40 | - | - | - | - | - | 76 | - | - | - |100 | - | - | - | - |
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ5 | 23 | 29 | - | 41 | - | - | - | - | - | 77 | - | - | - |101 | - | - | - | - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ6 | 24 | - | - | 42 | - | 54 | - | - | 72 | 78 | - | 90 | 96 | - | - | - | - | 114|
=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
Δ7 | 25 | - | - | 43 | - | 55 | - | - | 73 | 79 | - | 91 | 97 | - | - | - | - | - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ8 | - | - | - | 44 | - | 56 | - | - | - | 80 | - | 92 | - | - | - | - | - | - |
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ9 | - | - | - | 45 | - | 57 | - | - | - | 81 | - | 93 | - | - | - | - | - | - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ10 | - | - | - | 46 | 52 | 58 | - | 70 | - | 82 | 88 | 94 | - | - | - | - | 112| - |
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ11 | - | - | - | 47 | 53 | 59 | - | 71 | - | 83 | 89 | 95 | - | - | - | - | 113| - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ T
Δ12 | - | - | - | 48 | - | 60 | 66 | - | - | 84 | - | - | - | - | - | 108| - | - | H
=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+ E
Δ13 | - | - | - | 49 | - | 61 | 67 | - | - | 85 | - | - | - | - | - | 109| - | - |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ P
Δ14 | - | - | 32 | 50 | - | 62 | 68 | - | - | 86 | - | - | - | - | - | 110| - | - | O
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ W
Δ15 | - | - | 33 | 51 | - | 63 | 69 | - | - | 87 | - | - | - | - | - | 111| - | - | E
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ R
Δ16 | - | - | 34 | - | - | 64 | - | - | - | - | - | - | - | - | 106| - | - | - |
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ O
Δ17 | - | - | 35 | - | - | 65 | - | - | - | - | - | - | - | - | 107| - | - | - | F
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
Δ18 | - | 30 | 36 | - | - | - | - | - | - | - | - | - | - |102 | -| - | - | - | ∑=168
=====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+====+
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16| 17| 18 | 19 | V
-----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+----+ S
| Δ Δ | Φ12 | Δ Δ |
113 150 ≜114-25 557 619 = 1+618
```

[![eQ19](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)
](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-entrypoint-md)

![HxD](https://user-images.githubusercontent.com/8466209/205026477-b05094ce-fe6f-46d3-a579-50f407f42c70.png)

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[![factorcode](https://user-images.githubusercontent.com/8466209/205431165-24d484fc-c7a2-4482-b2c2-61de97495a67.png)](https://docs.factorcode.org/content/article-vocab-index.html)

[![TA_Chart](https://user-images.githubusercontent.com/8466209/204839094-d6b1713d-af4e-4fee-b073-3fe84e1e9275.png)](https://tfhub.dev/)

[![2022-11-30 (5)](https://user-images.githubusercontent.com/8466209/205431468-6777265f-63a8-42ea-b454-d45227478362.png)
](https://github.com/factor/factor/)
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![integration](https://user-images.githubusercontent.com/8466209/204819549-e0190e18-035d-4093-b6c7-3315d355f160.jpg)

![integration](https://user-images.githubusercontent.com/8466209/204817921-7b3cb166-dd8a-49b0-8c13-915f7aa9b210.jpg)

[![default](https://user-images.githubusercontent.com/8466209/202907299-bcd8f3b9-51db-42f8-a9e6-0c9a9da0cadf.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-hexagon-md)

[![default](https://user-images.githubusercontent.com/8466209/202907392-215918c3-84f5-4b14-a016-79b9d3e1f76f.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-output-md)

![TA_Chart](https://user-images.githubusercontent.com/8466209/204747440-0950b4e4-724a-43c9-92ce-86838e682128.png)
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![202907558-c7198082-14fd-409b-9e31-1a0440f79039](https://user-images.githubusercontent.com/8466209/204255750-5aae0f08-89ba-406b-b38f-6100a38a0280.png)![image](https://user-images.githubusercontent.com/8466209/202908203-6a7fdaa1-2e75-4658-aa9d-a298292a3065.png)

![default](https://user-images.githubusercontent.com/8466209/202907739-d8821b4d-47a8-41a8-bd43-e1dad600481c.png)

[![202907558-c7198082-14fd-409b-9e31-1a0440f79039](https://user-images.githubusercontent.com/8466209/204256833-d12508ae-8cb1-4381-ade5-7acfcc3f0e12.png)](https://github.com/kaustubhcs/prime-hexagon)

[![default](https://user-images.githubusercontent.com/8466209/203874936-9065fbff-25f6-4357-a37b-6945502161d5.png)](https://gist.github.com/eq19/4ffc4d02579d5cfd336a553c6da2f267#file-keyring-md)
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![image](https://user-images.githubusercontent.com/8466209/202908132-ee24eacf-581d-479f-932a-5c0ff231198e.png)

[![image](https://user-images.githubusercontent.com/8466209/202908542-c67e33e7-56d4-4e6e-9513-58a5de0f436c.png)](https://gist.github.com/eq19/54600a56d20163c2da8910dd804ec406)

```liquid
|
| ----------- 5 -----------
| | |
↓ ↑ ↓
| mapping | feeding | lexering | parsering | syntaxing | grammaring |
|------------- 36' --------------|----------------------------36' ----------------------------|
| 19' | 17' | 13' | 11' | 7' | 5' |
+----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
+----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
| 2 | 60 | 40 | 1 | 30 | 30 | 5 | 1 | 30 | 200 | 8 | 40 | 50 | 1 | 30 | 200 | 8 | 10 | 40 |
+----+----+----+---+----+----+---+---+----+-----+----+----+----+----+----+-----+----+----+----+
↓ ↑ | |
| | | |
------------ 10 ------------- | |
↓ ↓ |
+----+----+----+---+----+----+---+
| 2 | 60 | 40 | 1 | 30 | 30 | 5 |
+----+----+----+---+----+----+---+
| | |
2+100 ◄-
-----------------------+----+----+----+----+----+----+----+----+----+----- |
True Prime Pairs Δ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum |
=======================+====+====+====+====+====+====+====+====+====+===== ↓
19 → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th ◄- 4 = π(10)
-----------------------+----+----+----+----+----+----+----+----+----+-----
```
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*****∑11(40,30,20) = 90*****

![default](https://user-images.githubusercontent.com/8466209/202907770-85d847b3-70c2-4f98-bd41-419a60b4e7b7.png)

![default](https://user-images.githubusercontent.com/8466209/202908008-13ffc49a-3c98-4d6a-8c81-49000c906224.png)

![default](https://user-images.githubusercontent.com/8466209/202907847-15b83802-b647-4c70-8bca-0db0ffa29ca6.png)

```
---+-----+-----
1 | 1 | 18
---+-----+-----
2 | 19 | 29
---+-----+-----
3 | {30}|{43}
---+-----+-----
```

![rep fork](https://user-images.githubusercontent.com/8466209/206839286-d3a9b366-fbd1-4953-badd-c760eeb07436.png)

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![cubes](https://user-images.githubusercontent.com/8466209/205804217-313e8f74-56d1-4401-be92-e3d3c95da055.jpg)

![prime](https://user-images.githubusercontent.com/36441664/87958552-dea18f80-cadb-11ea-9499-6c2ee580a5ca.png)

![ulam](https://upload.wikimedia.org/wikipedia/commons/2/25/Hexgrid_prime_number_spiral.svg)
[![default](https://user-images.githubusercontent.com/8466209/205531184-66086f89-ee4b-4536-9e22-9b1dc946b21e.png)](https://gist.github.com/eq19/f78d4470250720fb18111165564d555f#file-default-md)

![lexer](https://user-images.githubusercontent.com/8466209/204159538-6f87b60c-6a32-486d-aa55-c9af2db7eda6.png)
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