# The Search for The Graviton (spin 6)

Most theories containing gravitons suffer from severe problems. This has led theorists to make choices subjectively (as always) on what is the most elegant theory.

Tip

This section is referring to wiki page-17 of gist section-13 that is inherited from the gist section-24 by prime spin-108 and span-6 with the partitions as below.

It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way.

## Boson Decay

Higgs boson decay process into two Z bosons, each decaying in to two leptons. When a particle decays, it transforms into other particles (called decay products).

Note

Attempts to extend the Standard Model or other quantum field theories by adding gravitons run into serious theoretical difficulties at energies close to or above the Planck scale.

• This is because of infinities arising due to quantum effects; technically, gravitation is not renormalizable.
• Since classical general relativity and quantum mechanics seem to be incompatible at such energies, from a theoretical point of view, this situation is not tenable.

One possible solution is to replace particles with strings. String theories are quantum theories of gravity in the sense that they reduce to classical general relativity plus field theory at low energies, but are fully quantum mechanical, contain a graviton, and are thought to be mathematically consistent. (Wikipedia)

There are 5 different string theories, each requiring 10 dimensions. On the other hand, string theory is supposed to be fundamental theory.

Warning

Introduced earlier in GUTS: The Unification of Forces Superstring theory is an attempt to unify gravity with the other three forces and, thus, must contain quantum gravity.

• The main tenet of Superstring theory is that fundamental particles, including the graviton that carries the gravitational force, act like one-dimensional vibrating strings.
• Since gravity affects the time and space in which all else exists, Superstring theory is an attempt at a Theory of Everything (TOE).
• Each independent quantum number is thought of as a separate dimension in some super space (analogous to the fact that the familiar dimensions of space are independent of one another) and is represented by a different type of Superstring.
• As the universe evolved after the Big Bang and forces became distinct (spontaneous symmetry breaking), some of the dimensions of superspace are imagined to have curled up and become unnoticed.
• Forces are expected to be unified only at extremely high energies and at particle separations on the order of 10^-35m. This could mean that Superstrings must have dimensions or wavelengths of this size or smaller.
• Just as quantum gravity may imply that there are no time intervals shorter than some finite value, it also implies that there may be no sizes smaller than some tiny but finite value. That may be about 10^-35m.
• If so, and if Superstring theory can explain all it strives to, then the structures of Superstrings are at the lower limit of the smallest possible size and can have no further substructure.
• This would be the ultimate answer to the question the ancient Greeks considered: There is a finite lower limit to space. Not only is Superstring theory in its infancy, it deals with dimensions about 17 orders of 10^-18m magnitude smaller than the details that we have been able to observe directly.
• It is thus relatively unconstrained by experiment, and there are a host of theoretical possibilities to choose from. This has led theorists to make choices subjectively (as always) on what is the most elegant theory, with less hope than usual that experiment will guide them.
• It has also led to speculation of alternate universes, with their Big Bangs creating each new universe with a random set of rules. These speculations may not be tested even in principle, since an alternate universe is by definition unattainable. It is something like exploring a self-consistent field of mathematics, with its axioms and rules of logic that are not consistent with nature.

Such endeavors have often given insight to mathematicians and scientists alike and occasionally have been directly related to the description of new discoveries. (College Physics 2e - pdf page 1518)

Note

With William Thomson’s idea of vortex atoms coming of age in the shape of string and superstring theories, in recent years hopes for a \$nite theory of quantum gravity have centered on the quantum superstring (QSS).

• Although the perturbation expansion yields finite terms, the summations do involve infinities [ 2481. However, that would still be true in quantum electrodynamics (QED) ; in perturbative treatments in quantum field theory these infinities are assumed to arise because of non-perturbative solutions and are regarded as an indication of the latter’s existence. Should we then consider the search for a theory of quantum gravity as having reached its goal and should we therefore cross it out as a motivation for the study of non-Riemannian gravitational theories?
• The basic assumption in the post- 1984 treatment of the quantum superstring [ 2381 “theory of everything” (TOE), an on-mass-shell S-matrix type theory, is that its truncation below Planck mass should go over smoothly into an off-mass-shell relativistic quantum (point) local field theory * (including a version of ten-dimensional supergravity, in one sector of the “heterotic string” [ 2471, for instance) thus, even if the search were over, the same geometrical-gravitational question then relates to that truncated “low-energy” field theory and its gravitational sector.

Moreover, it has been pointed out [ 1051 that consistency would then require the low-energy \$eid theory to be fmite by itseIf! This then implies the existence of a finite or renormalizable relativistic quantum field theory of gravity. (Gauge theory of gravity - pdf)

The symmetry of this supergravity theory is given by the supergroup OSp(1\32) which gives the subgroups O(1) for the bosonic and Sp(32) for the fermion.

Note

In general relativity, gravity is a force that bends and warps space-time around supermassive bodies.

• Even though gravity is one of the four fundamental forces in nature, it is very weak compared to the other three forces (electromagnetism, weak force and strong force). So it can’t be observed or identified on the scale of subatomic particles.
• However, gravity is very dominant in long-distance scenarios. It controls the structure of the macro universe (galaxies, planets, stars, moons).
• As far as quantum mechanics is concerned, gravity doesn’t have much effect. The probable nature of the quantum realm also poses a significant challenge for the induction of gravity in the quantum realm.
• Generally, gravity does not act as a particle as its own. Even if a hypothetical model is introduced to explain the particle nature of a gravity particle, it violates fundamental energy laws.

In the 1970s, theorists tried to discard the self-destructive idea of point-like gravity particles. Instead of point particles, strings were introduced. Even if strings collide, there will be no infinite energy problem. Strings can smoothly smash and rebound without implying any physically nonsense infinities.

This standard model is missing the Gravitational interaction and it is postulated that there exists a particle called the Graviton that leads to supergravity theory.

Note

Supergravity is an extension of supersymmetry, designed to include the principles of General Relativity. In order to make this possible, supersymmetry has to become local, with a spacetime-dependent spinor ǫ(x) parametrising the infinitesimal SUSY transformation.

• The key ingredient of supergravity is the graviton hµν , a massless spin-2 elementary particle which couples to the stress-energy tensor, thus mediating gravitational interactions.
• Its fermionic, spin-3/2 partner, the gravitino ψαµ, equipped both with a spinor index α and a spacetime index µ, is the gauge field of local supersymmetry and becomes massive when SUSY is broken, by absorbing the emerging goldstino in the so-called super-Higgs mechanism.
• There are two ways in which the graviton can be related to the metric gµν, either through an infinitesimal expansion gµν = ηµν + hµν around the flat metric ηµν , or through the vielbein formalism.

As is well-known from General Relativity, the metric (and implicitly the graviton) has tosatisfy the Einstein’s field equations (Holomorphic_Yukawa_Couplings - pdf)

Note

Think of it this way, all gravitating bodies in the universe would be surrounded at all times by a cloud of tunneling electrons. We cannot see these particles since they’re so small and since they permeate all of space. They would also tunnel to a different location about once every Planck time (about 10^-43 seconds) whenever they interact with another particle.

• These interactions between particles amount to the exchanges of bosons between electrons and other electrons or other fermions. At each point where the electron absorbs another boson, we say that the wave function of the electron collapses, and it tunnels to a new location whereupon it interacts with yet another particle.
• The cloud of electron surrounding gravitating objects would diminish in inverse proportion to the square of the distance; hence, if you recede from an objects’ surface, you’re less likely to find an electron tunneling from that object.
• Electrons also make an excellent candidate for a particle of gravity since they absorb and emit photons readily, and we know from Einstein’s theory of general relativity that light interacts readily with gravitational fields, and that gravitational fields are thought to emit photons spontaneously.
• This spontaneous emission of photons is what we refer to as the cosmological constant or dark energy, and in our current thinking on the topic we imagine that particles of antimatter are created and annihilate with particles of matter leading, occasionally, to the emission of a photon. I suspect that this is incorrect and that no such thing as antimatter really exists. I suspect that positrons are really tunneling W particles and that this Dirac Sea, or background of tunneling electrons, is really giving rise to this phenomenon of the cosmological constant, or vacuum energy, we observe inn nature.
• As a consequence, we would need to adumbrate our standard model of particle physics by about half. This ought to be seen as a positive thing in physics. No longer do we have untestable assumptions (such as the creation and annihilation of particles) in our models, and we have a far easier means of now beginning to probe the quantum nature of gravity.

The other fascinating consequence of this way of thinking is that gravity would no longer be a fundamental force; instead it would be a secondary effect of electromagnetism. This should have been what we anticipated all along; and now, we might have a quantum theory focusing on only three forces and a theory of gravitation that is truly particle-based. (Medium - Article)

Note

There are two groups of scientists (called collaborations) looking for evidence of gravitons in proton-proton collision experiments at the Large Hadron Collider at CERN. Once a graviton has been created, it’s expected to decay in one of a few possible ways - and it’s evidence of these decays that the collaborations are looking for. ATLAS search for evidence that the gravitons decays into two photons, and the CMS search for evidence that the graviton decays into two jets (bursts) of hadrons (a particular class of particle). (ThingsWeDontKnow.com)

## Prime Assessments

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 ◄--- #43 ◄--- 24s 👈 30 ✔️
8 13 5 1 0 13 ◄--- #17 ◄--- #49 ◄--- 32s 👈 30 ✔️
9 17 0 1 1 17 ◄--- 7th prime 👈 5 ◄--- 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
-----

Lightning speed ÷ Shockwave speed = 300000km/s ÷ 3km/s = 100000 ÷ 1

Sub  | i  |     β | f
=======+====+=======+=======  ===   ===   ===   ===   ===   ===
1:1:0 | 1  |     1 | 2 {71}   1     1     |     |     |     |
-------+----+-------+-------  ---   ---    |     |     |     |
1:2:1 | 2  |     2 | 3 {71}         |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
*1:2:2 | 3  |     3 | 7 = 1 + 2x3    |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
*1:3:3 | 4  |     4 | 10 = 9 + 1     |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
1:3:4 | 5  |     5 | 11 = 9 + 2     |     |     |     |     |
-------+----+-------+----            9     1‘    |    Δ100   |
*1:3:5 | 6  |     6 | 12 = 9 + 3     |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
*1:4:6 | 7  |     7 | 13 = 9 + 4     |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
1:4:7 | 8  |     8 | 14 = 9 + 5     |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
*1:4:8 |{9} |     9 | 15 = 9 + 6     |     |     |     |     |
-------+----+-------+----            |     |     |     |     |
*1:4:9 |{10}|    10 | 19 = 9 + 10    |     |     |     |     |
=======+====+=======+====           ===   ---    1"   ---    |
2:1:0 | 11 |    20 | 20 = 19 + log 10¹    |     |     |     |
-------+----+-------+----                  |     |     |     |
2:2:1 | 12 |    30 | 26 = 20 + 2x3        |     |     |     |
-------+----+-------+----                  |     |     |     |
*2:2:2 | 13 |    40 | 27 = 26 + 1          |     |     |     |
-------+----+-------+----                  |     |     |     |
*2:3:3 | 14 |    50 | 28 = 26 + 2          |     |     |     |
-------+----+-------+----                  |     |     |     |
2:3:4 | 15 |    60 | 29 = 26 + 3          9‘    |   Δ200    |
-------+----+-------+----                  |     |     |     |
*2:3:5 | 16 |    70 | 30 = 26 + 4          |     |     |     |
-------+----+-------+----                  |     |     |     |
*2:4:6 | 17 |    80 | 31 = 26 + 5          |     |     |     |
-------+----+-------+----                  |     |     |     |
2:4:7 |{18}|    90 | 32 = 26 + 6          |     |     |     |
-------+----+-------+----                  |     |     |     |
*2:4:8 |{19}|   100 | 36 = 26 + 10         |     |     |     |
=======+====+=======+====                 ===   ---   ---  ∆1000
*2:4:9 | 20 |   200 | 38 = 36 + log 10²          |     |     |
-------+----+-------+----                        |     |     |
3:1:0 | 21 |   300 | 40 = 36 + 2 x log 10²      |     |     |
-------+----+-------+----                        |     |     |
3:2:1 | 22 |   400 | 41 = 40 + 1                |     |     |
-------+----+-------+----                        |     |     |
*3:2:2 | 23 |   500 | 42 = 40 + 2                |     |     |
-------+----+-------+----                        |     |     |
*3:3:3 | 24 |   600 | 43 = 40 + 3                9"  Δ300    |
-------+----+-------+----                        |     |     |
3:3:4 | 25 |   700 | 44 = 40 + 4                |     |     |
-------+----+-------+----                        |     |     |
*3:3:5 | 26 |   800 | 45 = 40 + 5                |     |     |
-------+----+-------+----                        |     |     |
*3:4:6 | 27 |   900 | 46 = 40 + 6                |     |     |
-------+----+-------+----                        |     |     |
3:4:7 |{28}|  1000 | 50 = 40 + 10               |     |     |
=======+====+=======+====                       ===  ====    |
*3:4:8 |{29}|  2000 | 68 = 50 + 3 x (2x3)      {10³}   |     |
-------+----+-------+----                        Δ     |     |
3:4:9 |{30}|  3000 |{71}= 68 + log 10³                |     |
-------+----+-------+----                              |     |
3:2:1 | 31 |  4000 | 72 = 71 + 1                      |     |
-------+----+-------+----                              |     |
*3:2:2 | 32 |  5000 | 73 = 71 + 2                      |     |
-------+----+-------+----                              |     |
*3:3:3 | 33 |  6000 | 74 = 71 + 3                    Δ400    |
-------+----+-------+----                              |     |
3:3:4 | 34 |  7000 | 75 = 71 + 4                      |     |
-------+----+-------+----                              |     |
*3:3:5 | 35 |  8000 | 76 = 71 + 5                      |     |
-------+----+-------+----                              |     |
*3:4:6 | 36 |  9000 |{77}= 71 + 6                      |     |
-------+----+-------+----                              |     |
3:4:7 |{37}| 10000 | 81 = 71 + 10 = 100 - 19          |     |
=======+====+=======+====                             ====  ----

32-5 = 27 = 9x3

Note

The four faces of our pyramid additively cascade 32 four-times triangular numbers (Note that 4 x 32 = 128 = the perimeter of the square base which has an area of 32^2 = 1024 = 2^10). These include Fibo1-3 equivalent 112 (rooted in T7 = 28; 28 x 4 = 112), which creates a pyramidion or capstone in our model, and 2112 (rooted in T32 = 528; 528 x 4 = 2112), which is the index number of the 1000th prime within our domain, and equals the total number of ‘elements’ used to construct the pyramid. (PrimesDemystified)

Note

While gravitons are presumed to be massless, they would still carry energy, as does any other quantum particle. Photon energy and gluon energy are also carried by massless particles.

• It is unclear which variables might determine graviton energy, the amount of energy carried by a single graviton.
• Alternatively, if gravitons are massive at all, the analysis of gravitational waves yielded a new upper bound on the mass of gravitons.
• The graviton’s Compton wavelength is at least 1.6×10^16 m, or about 1.6 light-years, corresponding to a graviton mass of no more than 7.7×10−23 eV/c2.[22]
• This relation between wavelength and mass-energy is calculated with the Planck–Einstein relation, the same formula that relates electromagnetic wavelength to photon energy.
• However, if gravitons are the quanta of gravitational waves, then the relation between wavelength and corresponding particle energy is fundamentally different for gravitons than for photons, since the Compton wavelength of the graviton is not equal to the gravitational-wave wavelength.
• Instead, the lower-bound graviton Compton wavelength is about 9×109 times greater than the gravitational wavelength for the GW170104 event, which was ~ 1,700 km. The report[22] did not elaborate on the source of this ratio.

It is possible that gravitons are not the quanta of gravitational waves, or that the two phenomena are related in a different way. (Wikipedia)

Double decay generations = 2^π(11 dimensions) = 2⁵ = 32

E = mc²
m = E/c²

c = 1 light-second
= 1000 years x L / t
= 12,000 months x 2152612.336257 km / 86164.0906 sec
= 299,792.4998 km / sec

Note:
1 year = 12 months
1000 years = 12,000 months
Te = earth revolution = 365,25636 days
R = radius of moon rotation to earth = 384,264 km
V = moon rotation speed = 2πR/Tm = 3682,07 km/hours
Ve = excact speed = V cos (360° x Tm/Te) = V cos 26,92848°
Tm = moon revolution (sidereal) = 27,321661 days = 655,719816 hours
t = earth rotation (sinodik) = 24 hours = 24 x 3600 sec = 86164.0906 sec
L = Ve x Tm = 3682,07 km/hours x cos 26,92848° x 655,71986 = 2152612.336257 km

Conclusion:
π(π(π(π(π(32(109²-89²)))))) Universe vs Unknown vs Unknowns (5th level) ✔️
👇
π(π(π(π(32(109²-89²))))) Galaxies vs Universe vs Unknown ✔️
👇
π(π(π(32(109²-89²)))) Sun vs Galaxies vs Universe ✔️
👇
π(π(32(109²-89²))) Moon vs Sun vs Galaxies ✔️
👇
|--👇---------------------------- 2x96 ---------------------|
|--👇----------- 7¤ ---------------|---------- 5¤ ----------|
|- π(32(109²-89²))=109² -|-- {36} -|-------- {103} ---------|
+----+----+----+----+----+----+----+----+----+----+----+----+
|  5 |  7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 |{43}|
+----+----+----+----+----+----+----+----+----+----+----+----+
|--------- {53} ---------|---- {48} ----|---- {48} ----|109²-89² 👉 Unknown ✔️
|---------- 5¤ ----------|------------ {96} -----------|-1¤-|
|-------- Bosons --------|---------- Fermions ---------|-- Graviton
13 variations               48 variations           11 variations

BBC News: Prof Stephen Hawking's final research paper suggests that our Universe may be one of many similar. This paper is the fruit of 20 years' work.

## Parity Order

Note

In the second opposing term, the position 13 gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 31 as the 11th prime number is now forced as a new axis-symmetrical zero position. (Google Patent DE102011101032A9)

s(18) = 1 + 49 = 68 - 18 = 50

∆9 (local) + 2×∆9 (decay) = ∆27

The Prime Recycling ζ(s):
(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**

----------------------+-----+-----+-----+                                    ---
7 --------- 1,2:1|   1 |  30 |  40 | 71 (2,3) ‹-------------@----        |
|                +-----+-----+-----+-----+                        |      |
|  8 ‹------  3:2|   1 |  30 |  40 |  90 | 161 (7) ‹---           |      5¨
|  |             +-----+-----+-----+-----+             |          |      |
|  |  6 ‹-- 4,6:3|   1 |  30 | 200 | 231 (10,11,12) ‹--|---       |      |
|  |  |          +-----+-----+-----+-----+             |   |      |     ---
--|--|-----» 7:4|   1 |  30 |  40 | 200 | 271 (13) --›    | {5®} |      |
|  |          +-----+-----+-----+-----+                 |      |      |
--|---› 8,9:5|   1 |  30 | 200 | 231 (14,15) ---------›       |      7¨
289        |          +-----+-----+-----+-----+-----+                  |      |
|          ----› 10:6|  20 |   5 |  10 |  70 |  90 | 195 (19) --› Φ   | {6®} |
--------------------+-----+-----+-----+-----+-----+                  |     ---
67 --------› 11:7|   5 |   9 |  14 (20) --------› ¤               |      |
|                +-----+-----+-----+                              |      |
|  78 ‹----- 12:8|   9 |  60 |  40 | 109 (26) «------------       |     11¨
|  |             +-----+-----+-----+                       |      |      |
|  |  86‹--- 13:9|   9 |  60 |  69 (27) «-- 2×Δ9 (2×MEC30) | {2®} | ✔️   |
|  |  |          +-----+-----+-----+                       |      |     ---
|  |   ---› 14:10|   9 |  60 |  40 | 109 (28) -------------       |      |
|  |             +-----+-----+-----+                              |      |
|   ---› 15,18:11|   1 |  30 |  40 | 71 (29,30,31,32) ----------        13¨
329  |                +-----+-----+-----+                                     |
|   ‹--------- 19:12|  10 |  60 | {70} (36) ‹--------------------- Φ        |
-------------------+-----+-----+                                          ---
786 ‹------- 20:13|  90 |  90 (38) ‹-------------- ¤                      |
|                +-----+-----+                                           |
| 618 ‹- 21,22:14|   8 |  40 |  48 (40,41) ‹----------------------      17¨
|  |             +-----+-----+-----+-----+-----+                  |      |
|  | 594 ‹- 23:15|   8 |  40 |  70 |  60 | 100 | 278 (42) «--     |{6'®} |
|  |  |          +-----+-----+-----+-----+-----+             |    |     ---
--|--|-»24,27:16|   8 |  40 |  48 (43,44,45,46) ------------|----       |
|  |          +-----+-----+                               |           |
--|---› 28:17| 100 | {100} (50) ------------------------»           19¨
168        |          +-----+                                                 |
|         102 -› 29:18| 50  | 50(68) --> 3×∆9-∆9=Δ18 goes to unknown ✔️       |
----------------------+-----+                                                ---

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.
Note

Using Euler’s method to find p(40): A ruler with plus and minus signs (grey box) is slid downwards, the relevant terms added or subtracted. The positions of the signs are given by differences of alternating natural (blue) and odd (orange) numbers. In the SVG file, hover over the image to move the ruler (Wikipedia).

π(π(π(1000th prime))) + 1 = 40

## Distribution Order

169 - 1 cycle of 360° = 169 - ∆1 = 168 = π(1000)

Note

The primary reason that the electron is considered to be elementary is that experimentally it appears to be point-like and hence structureless.

• At the same time we are confronted with the fact that it has a rich set of properties which are fundamental to its nature.
• It has an elementary charge, a half-integral spin, a de nite mass, a well de ned dipole moment, an anomalous spin factor g-2 and of course a wave-particle nature.

It seems inappropriate to think about such things as the elementary charge as a separate building block from the elementary particle which carries it. (Is the electron a photon with toroidal topology? - pdf)

Fermion  | spinors | charged | neutrinos |   quark   | components | parameter
Field   |   (s)   |   (c)   |    (n)    | (q=s.c.n) |  Σ(c+n+q   | (complex)
===========+=========+=========+===========+===========+============+===========
bispinor-1 |    2    |    3    |     3     |    18     |     24     |   19
-----------+---------+---------+-----------+-----------+------------+-- 17
bispinor-2 |    2    |    3    |     3     |    18     |     24     |   i12 ✔️
===========+=========+=========+===========+===========+============+===========
bispinor-3 |    2    |    3    |     3     |    18     |     24     |   11
-----------+---------+---------+-----------+-----------+------------+-- 19
bispinor-4 |    2    |    3    |     3     |    18     |     24     |   i18 ✔️
===========+=========+=========+===========+===========+============+===========
SubTotal |    8    |   12    |    12     |    72     |     96     |   66+i30
===========+=========+=========+===========+===========+============+===========
majorana-1 |   2x2   |    -    |    18     |     -     |     18     |   18 ✔️
-----------+---------+---------+-----------+-----------+------------+-----------
majorana-2 |   2x2   |    -    |    12     |     -     |     12     |   12 ✔️
-----------+---------+---------+-----------+-----------+------------+-----------
majorana-3 |   2x2   |    -    |    13     |     -     |     13     |   i13
===========+=========+=========+===========+===========+============+===========
SubTotal |    12   |    -    |    43     |     -     |     43     |  30+i13
===========+=========+=========+===========+===========+============+===========
Total |    20   |   12    |    55     |    72     |    139     |  96+i43 ✔️
Note

Folio math is similar to modular math, but instead of the numbers wrapping around or spinning around a unit circle, they turn back at different positions on both the X and Y axis. In other words, they never make full cycles.

• The Y-Axis splits at the top, and the X-Axis splits on the left. The colors help this stand out. Let’s start with the top of the Y-Axis. All digits at the top of the Y-Axis reduce down to 1,7,4 or 5,2,8.
• This is important. Using this Prime Number Folio Coordinate System, it’s easier to think of prime numbers in separate sequences across from each other and right or left-handed rather than next to each other on a number line. I see them as Chiral.
• All digits in on the right-hand side of the Y-Axis reduce down to 5, 2 or 8. (For example 179 has 3 digits, what matters is that the numbers 1 +7+9 sum to the number 8.) So this would be considered a right-handed prime number. Or a number on the right side of the Y-Axis.

The image stands on its own. The patterns should jump off the page. Especially with the color. Right-handed numbers have different properties than the left-handed numbers. These observations are in no way mathematically rigorous.

• The numbers on the right side (5,2,8)| of the Y-Axis include not only prime numbers, but the products of the prime numbers combined from both sides of the Y-axis.
• Every product on the right-hand side of the Y-Axis is created from two primes (or semi-primes or combination of semi-primes) from both sides of the Y-axis (one from each side), which ALWAYS sum to an exact multiple of 6. These are plotted on the right side of the X-Axis. (For example 7×11=77. While 7+11=18.)

Using this Folio Coordinate System, it’s easy to see how the products and sums and their distribution are directly related to each other. You might want to start thinking about the Goldbach Conjecture.

• All products and sums on the right side are indigo/purple to show how they combine with the red and blue prime numbers.
• It looks like we are simply adding 6 to each Axis/number line, when in fact we are adding the number 1 to each consecutive number but positioning it at different points while moving around both the X and Y Axis.

The number 35 is an important number. It’s the first number on the right-hand side that’s a product of two prime factors of 5 x 7 = 35.

• The sum of 5 + 7 = 12. Since the right-handed numbers are distributed evenly by 6, we can add 7 x 6 = 42 to 35 and land on the number 77.
• So now we know that starting with the number 35 if we add 42 continuously we will NEVER land on a prime number. We can also add 5 x 6 = 42 to 35 and land on 65.
• We also know that 7 + 11 = 18. The next number that introduces a product of two primes is 5 x 13 = 65 and 5 + 13 = 18. So we can take 6 x 13 = 78 and add this to 65 and land on 143. Which is the product of 11 x 13 = 143.
• Starting with 65 we can add 78 continuously and NEVER land on a prime number.
• In the meantime 77 (The product of 7 and 11 now introduces the prime number 11 into the mix. So 77 + (6x11) = 143.
• Starting with 77 we can add 66 continuously and NEVER land on a prime number.

You can’t add multiples of 6 until that multiple is introduced into the sequence. The primes on the left behave differently. You can still move around using multiples of 6, but there is no common starting point like the number 35.

• You have to start with the squares of 5 at 25 (in blue) for one sequence of numbers and the square of 7 at 49 (in red) for the other sequence of numbers.
• The sums of these products are also not exact multiples of 6. They sum to 10 and 14 and are matched to the split X Axis on the left-hand side of the graph.

The Prime Number Folio Coordinate System and it’s natural numbers are all you need to find a prime number or a composite number and it’s factors. No need for complex numbers or the Reimann Hypothesis. (Medium)

Being brought forth you will also begin to uncover the irrelevant role that the Riemann hypothesis plays 7 ate 9 in understanding this elegant distribution.

Note

This curve is a polar plot of the first 20 non-trivial Riemann zeta function zeros including Gram points along the critical line ζ(1/2+t) for real values of t running from 0 to 50. The consecutive zeros have 50 red plot points between each with zeros identified by magenta concentric rings (scaled to show the relative distance between their values of t). (Wikipedia)

20x10+ ½(16×6) + ¼(12×18) + ⅛(16×16) = 200 + 48 + 32 + 6 = 286 = 2 x 11 x 13

Despite there are many studies and papers it is still an important open problem today.

Warning

The solution is not only to prove Re(z)= 1/2 but also to calculate ways for the imaginary part of the complex root of ζ(z)=0 and also to solve the functional equations. (Riemann Zeta - pdf)

Sehr leider Herr Riemann. Bis jetzt Leute können den Fall immer noch nicht lösen.