The Prime Recycling ζ(s)
This section is referring to wiki page-7 of gist section-3 that is from the gist section-37 by prime spin-13 and span- with the partitions as below.
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The Position Pairs
36 + 36 - 6 partitions = 72 - 6 = 66 = 30+36 = 6x11
$True Prime Pairs:
(5,7), (11,13), (17,19)
layer| i | f
-----+-----+---------
| 1 | 5
1 +-----+
| 2 | 7
-----+-----+--- } 36 » 6®
| 3 | 11
2 +-----+
| 4 | 13
-----+-----+---------
| 5 | 17
3 +-----+ } 36 » 6®
| 6 | 19
-----+-----+---------
#!/usr/bin/env python
import numpy as np
from scipy import linalg
class SU3(np.matrix):
GELLMANN_MATRICES = np.array([
np.matrix([ #lambda_1
[0, 1, 0],
[1, 0, 0],
[0, 0, 0],
], dtype=np.complex),
np.matrix([ #lambda_2
[0,-1j,0],
[1j,0, 0],
[0, 0, 0],
], dtype=np.complex),
np.matrix([ #lambda_3
[1, 0, 0],
[0,-1, 0],
[0, 0, 0],
], dtype=np.complex),
np.matrix([ #lambda_4
[0, 0, 1],
[0, 0, 0],
[1, 0, 0],
], dtype=np.complex),
np.matrix([ #lambda_5
[0, 0,-1j],
[0, 0, 0 ],
[1j,0, 0 ],
], dtype=np.complex),
np.matrix([ #lambda_6
[0, 0, 0],
[0, 0, 1],
[0, 1, 0],
], dtype=np.complex),
np.matrix([ #lambda_7
[0, 0, 0 ],
[0, 0, -1j],
[0, 1j, 0 ],
], dtype=np.complex),
np.matrix([ #lambda_8
[1, 0, 0],
[0, 1, 0],
[0, 0,-2],
], dtype=np.complex) / np.sqrt(3),
])
def computeLocalAction(self):
pass
@classmethod
def getMeasure(self):
pass
Now the following results: Due to the convolution and starting from the desired value of the prime position pairs, the product templates and prime numbers templates of the prime number 7 lie in the numerical Double strand parallel opposite.
The Fourth Root
In number theory, the partition functionp(n) represents the number of possible partitions of a non-negative integer n.
Integers can be considered either in themselves or as solutions to equations (Diophantine geometry).
Young diagrams associated to the partitions of the positive integers 1 through 8. They are arranged so that images under the reflection about the main diagonal of the square are conjugate partitions (Wikipedia).
By parsering π(1000)=168 primes of the 1000 id’s across π(π(10000))-1=200 of this syntax then the (Δ1) would be initiated. Based on Assigning Sitemap priority values You may see them are set 0.75 – 1.0 on the sitemap’s index:
Priority Page Name
1 Homepage
0.9 Main landing pages
0.85 Other landing pages
0.8 Main links on navigation bar
0.75 Other pages on site
0.8 Top articles/blog posts
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0.4 – 0.7 Articles, blog posts, FAQs, etc.
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By this object orientation then the reinjected primes from the π(π(10000))-1=200 will be (168-114)+(160-114)=54+46=100. Here are our layout that is provided using Jekyll/Liquid to facilitate the cycle:
100 + 68 + 32 = 200
$True Prime Pairs:
(5,7), (11,13), (17,19)
layer | node | sub | i | f. MEC 30 / 2
------+------+-----+-----+------ ‹--------------------------- 30 {+1/2} √
| | | 1 | --------------------------
| | 1 +-----+ |
| 1 | | 2 | (5) |
| |-----+-----+ |
| | | 3 | |
1 +------+ 2 +-----+---- |
| | | 4 | |
| +-----+-----+ |
| 2 | | 5 | (7) |
| | 3 +-----+ |
| | | 6 | 11s
------+------+-----+-----+------ } (36) |
| | | 7 | |
| | 4 +-----+ |
| 3 | | 8 | (11) |
| +-----+-----+ |
| | | 9 |‹-- |
2 +------| 5* +-----+----- |
| | | 10 | |
| |-----+-----+ |
| 4 | | 11 | (13) --------------------- 32 √
| | 6 +-----+ ‹------------------------------ 15 {0} √
| | | 12 |---------------------------
------+------+-----+-----+------------ |
| | | 13 | |
| | 7 +-----+ |
| 5 | | 14 | (17) |
| |-----+-----+ |
| | | 15 | 7s = f(1000)
3* +------+ 8 +-----+----- } (36) |
| | | 16 | |
| |-----+-----+ |
| 6 | | 17 | (19) |
| | 9 +-----+ |
| | | 18 | -------------------------- 68 √
------|------|-----+-----+----- ‹------ 0 {-1/2} √
p r i m e s
1 0 0 0 0 0
2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
3 2 0 1 0 2 👉 2
4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40
6 👉 11s Composite Partition ◄--- 102 👈 4th spin
6 7 3 1 0 7 ◄--- #23 👈 7+23 = 30 ✔️
7 11 4 1 0 11 ◄--- #19 👈 11+19 = 30 ✔️
8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 13+17 = 30 ✔️
9 17 0 1 1 17 ◄--- 7th prime👈 17+7 != 30❓
18 👉 7s Composite Partition ◄--- 168 👈 7th spin
10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
-----
11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
..
..
40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
-----
41 167 0 1 1 ∆0
42 173 0 -1 1 ∆1
43 179 0 1 1 ∆2 ◄--- ∆∆1
44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
..
..
100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 👉 7s
-----
Composite System
By taking a distinc function between f(π) as P vs f(i) as NP where eiπ + 1 = 0 then theoretically they shall be correlated to get an expression of the prime platform similar to the Mathematical Elementary Cell 30 (MEC30).
∆17 + ∆49 = ∆66
p r i m e s
1 0 0 0 0 0
2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
3 2 0 1 0 2 👉 2
4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40
6 👉 11s Composite Partition ◄--- 102 👈 4th spin
6 7 3 1 0 7 ◄--- #23 👈 part of MEC30 ✔️
7 11 4 1 0 11 ◄--- #19 👈 part of MEC30 ✔️
8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 part of MEC30 ✔️
9 17 0 1 1 17 ◄--- 7th prime👈 not part of MEC30 ❓
18 👉 7s Composite Partition ◄--- 168 👈 7th spin
10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
-----
11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
..
..
40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
-----
41 167 0 1 1 ∆0
42 173 0 -1 1 ∆1
43 179 0 1 1 ∆2 ◄--- ∆∆1
44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
..
..
100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 👉 7s
-----
∆102 - ∆2 - ∆60 = ∆40
p r i m e s
1 0 0 0 0 0
2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
3 2 0 1 0 2 👉 2
4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40
6 👉 11s Composite Partition ◄--- 102 👈 4th spin
6 7 3 1 0 7 ◄--- #23 👈 30 ◄--- break MEC30 symmetry ✔️
7 11 4 1 0 11 ◄--- #19 👈 30 ✔️
8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 30 ✔️
9 17 0 1 1 17 ◄--- 7th prime👈 not part of MEC30 ❓
18 👉 7s Composite Partition ◄--- 168 👈 7th spin
10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
-----
11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
..
..
40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
-----
41 167 0 1 1 ∆0
42 173 0 -1 1 ∆1
43 179 0 1 1 ∆2 ◄--- ∆∆1
44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
..
..
100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 👉 7s
-----
The partitions of odd composite numbers (Cw) are as important as the partitions of prime numbers or Goldbach partitions (Gw). The number of partitions Cw is fundamental for defining the available lines (Lwd) in a Partitioned Matrix that explain the existence of partitions Gw or Goldbach partitions. (Partitions of even numbers - pdf)
30s + 36s (addition) = 6 x 11s (multiplication) = 66s
p r i m e s
1 0 0 0 0 0
2 1 0 0 0 1 ◄--- #29 ◄--- #61 👈 1st spin
3 2 0 1 0 2 👉 2
4 3 1 1 0 3 👉 89 - 29 = 61 - 1 = 60
5 5 2 1 0 5 👉 11 + 29 = 37 + 3 = 40
6 👉 11s Composite Partition ◄--- 102 👈 4th spin
6 7 3 1 0 7 ◄--- #23 👈 f(#30) ◄--- break MEC30 symmetry
7 11 4 1 0 11 ◄--- #19 👈 30
8 13 5 1 0 13 ◄--- #17 ◄--- #49 👈 30
9 17 0 1 1 17 ◄--- 7th prime 👈 f(#36) ◄--- antisymmetric state ✔️
18 👉 7s Composite Partition ◄--- 168 👈 7th spin
10 19 1 1 1 ∆1 ◄--- 0th ∆prime ◄--- Fibonacci Index #18
-----
11 23 2 1 1 ∆2 ◄--- 1st ∆prime ◄--- Fibonacci Index #19 ◄--- #43
..
..
40 163 5 1 0 ∆31 ◄- 11th ∆prime ◄-- Fibonacci Index #29 👉 11
-----
41 167 0 1 1 ∆0
42 173 0 -1 1 ∆1
43 179 0 1 1 ∆2 ◄--- ∆∆1
44 181 1 1 1 ∆3 ◄--- ∆∆2 ◄--- 1st ∆∆prime ◄--- Fibonacci Index #30
..
..
100 521 0 -1 2 ∆59 ◄--- ∆∆17 ◄--- 7th ∆∆prime ◄--- Fibonacci Index #36 👉 7s
-----
