Skip to content
eQuantum edited this page Sep 17, 2024 · 9 revisions

Prime Identity

We are going to assign prime identity as a standard model that attempts to stimulate a quantum field model called eQuantum for the four (4) known fundamental forces.

{% include list.liquid all=true %}

This presentation was inspired by theoretical works from Hideki Yukawa who in 1935 had predicted the existence of mesons as the carrier particles of strong nuclear force.

Addition Zones

Here we would like to explain the way of said prime identity on getting the arithmetic expression of an individual unit identity such as a taxicab number below.

It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician _[GH Hardy](https://en.wikipedia.org/wiki/G._H._Hardy)_ when he visited Indian mathematician _[Srinivasa Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan)_ in hospital _([Wikipedia](https://en.wikipedia.org/wiki/1729_(number)))_.

Ramanujan-Hardy number

These three (3) number are twin primes. We called the pairs as True Prime Pairs. Our scenario is mapping the distribution out of these pairs by taking the symmetrical behaviour of 36 as the smallest power (greater than 1) which is not a prime power.

The smallest square number expressible as the sum of **four (4) consecutive primes** in two ways (5 + 7 + 11 + 13 and 17 + 19) which are also **two (2) couples** of prime twins! _([Prime Curios!](https://en.wikipedia.org/wiki/1729_(number)](https://primes.utm.edu/curios/page.php?number_id=270)))_.
$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
 -----+-----+---------

Thus in short this is all about a method that we called as the 19 vs 18 Scenario of mapping the quantum way within a huge of primes objects (5 to 19) by lexering (11) the ungrammared feed (7) and parsering (13) across syntax (17).

Φ(1,2,3) = Φ(6,12,18) = Φ(13,37,61)

$True Prime Pairs:
(5,7), (11,13), (17,19)
 
layer | node | sub |  i  |  f
------+------+-----+----------
      |      |     |  1  | 
      |      |  1  +-----+          
      |  1   |     |  2  | (5)
      |      |-----+-----+
      |      |     |  3  |
  1   +------+  2  +-----+----
      |      |     |  4  |
      |      +-----+-----+
      |  2   |     |  5  | (7)
      |      |  3  +-----+
      |      |     |  6  |
------+------+-----+-----+------      } (36)
      |      |     |  7  |
      |      |  4  +-----+
      |  3   |     |  8  | (11)
      |      +-----+-----+
      |      |     |  9  |
  2   +------|  5  +-----+-----
      |      |     |  10 |
      |      |-----+-----+
      |  4   |     |  11 | (13)
      |      |  6  +-----+
      |      |     |  12 |
------+------+-----+-----+------------------
      |      |     |  13 |
      |      |  7  +-----+
      |  5   |     |  14 | (17)
      |      |-----+-----+
      |      |     |  15 |
  3   +------+  8  +-----+-----       } (36)
      |      |     |  16 |
      |      |-----+-----+
      |  6   |     |  17 | (19)
      |      |  9  +-----+
      |      |     |  18 |
------|------|-----+-----+------

The main background is that, as you may aware, the prime number theorem describes the asymptotic distribution of prime numbers which is still a major problem in mathematic.

Multiplication Zones

Instead of a proved formula we came to a unique expression called zeta function. This expression first appeared in a paper in 1737 entitled Variae observationes circa series infinitas.

This expression states that the sum of the zeta function is equal to the product of the reciprocal of one minus the reciprocal of primes to the powers. But what has this got to do with the primes?  The answer is in the following product taken over the primes p (discovered by _[Leonhard Euler](https://en.wikipedia.org/wiki/Leonhard_Euler)_):

zeta function

Meanwhile obtaining the non complex numbers it is easier to look at a graph like the one below which shows Li(x) (blue), R(x) (black), π(x) (red) and x/ln x (green); and then proclaim "R(x) is the best estimate of π(x)." Indeed it is for that range, but as we mentioned above, Li(x)-π(x) changes sign infinitely often, and near where it does, Li(x) would be the best value.

non complex numbers

And we can see in the same way that the function Li(x)-(1/2)Li(x1/2) is 'on the average' a better approximation than Li(x) to π(x); but no importance can be attached to the latter terms in Riemann's formula even by repeated averaging.

Exponentiation Zones

The problem is that the contributions from the non-trivial zeros at times swamps that of any but the main terms in these expansions.

A. E. Ingham says it this way: Considerable importance was attached formerly to a function suggested by Riemann as an approximation to π(x)... This function represents π(x) with astonishing accuracy for all values of x for which π(x) has been calculated, but we now see that its superiority over Li(x) ***is illusory***... and for special values of x (as large as we please) the one approximation will deviate as widely as the other from the true value _([primes.utm.edu](https://primes.utm.edu/howmany.html#better))_.

howmany primes

Moreover in it was verified numerically, in a rigorous way using interval arithmetic, that The Riemann hypothesis is true up to 3 · 10^12. That is, all zeroes β+iγ of the Riemann zeta-function with 0<γ≤3⋅1012 have β=1/2.

We have Λ ≤ 0.2. The next entry is conditional on taking H a little higher than 10*13, which of course, is not achieved by Theorem 1. This would enable one to prove Λ < 0.19. Given that our value of H falls between the entries in this table, it is possible that some extra decimals could be wrought out of the calculation. We have not pursued this _([arXiv:2004.09765](https://arxiv.org/abs/2004.09765))_.

functional equation

This Euler formula represents the distribution of a group of numbers that are positioned at regular intervals on a straight line to each other. Riemann later extended the definition of zeta(s) to all complex numbers (except the simple pole at s=1 with residue one). Euler's product still holds if the real part of s is greater than one. Riemann derived the functional equation of zeta function.

The Riemann zeta function has the trivial zeros at -2, -4, -6, ... (the poles of gamma(s/2)).  Using the Euler product (with the functional equation) it is easy to show that all the other zeros are in the critical strip of non-real complex numbers with 0 < Re(s) < 1, and that they are symmetric about the critical line Re(s)=1/2. The unproved Riemann hypothesis is that all of the nontrivial zeros are actually on the critical line _([primes.utm.edu](https://primes.utm.edu/notes/rh.html))_.

zeta function

This interpretation is consistent with interpreting the strings as World Lines of the Worlds of Many-Worlds Quantum Theory.

The 26-dimensional traceless subalgebra J3(O)o is arepresentation of the 26-dim Theory of Unoriented Closed Bosonic Strings produces a Bohm Quantum Theory with geometry of E6 / F4. The E6 of the can be represented in terms of:
- ***3 copies of the 26-dimensional*** traceless subalgebra J3(O)o of the 27-dimensional J3(O) by using the of ***78-dimensional E6 over 52-dimensional F4*** and the structure of based on the 26-dimensional representation of.
- In this view, Lie algebra D4-D5-E6-E7-E8 VoDou Physics model Jordan algebra fibration E6/F4 F4 as doubled J3(O)o F4 

In order to reproduce the known spectrum of weakly coupled bosonic string theory, bosonic M theory will have to contain an additional field besides the ***27 dimensional gravitational field***, namely a three-form potential CFT. _([PhiloPhysics - pdf](https://github.com/eq19/maps/files/14258292/PhiloPhysics.pdf))_

6+6 + 6/\6 = 6+6 + 15 = 27-day month

26 Dimensions of Bosonic String Theory

The areas of research, which involve about 30 research groups worldwide, share the basic physical assumptions and the mathematical description of quantum space.

Identition Zones

This issue is actually come from Riemann hypothesis, a conjecture about the distribution of complex zeros of the Riemann zeta function that is considered to be the most important of unsolved problems in pure mathematics.

In addition to the trivial roots, there also exist ***complex roots*** for real t. We find that the he first ten (10) non-trivial roots of the Riemann zeta function is occured when the values of t below 50. A plot of the values of ζ(1/2 + it) for t ranging from –50 to +50 is shown below. The roots occur each time ***the locus passes through the origin***. _([mathpages](https://www.mathpages.com/home/kmath738/kmath738.htm))_.

trivial roots

The path plan assume that a symmetric distribution of prime numbers with equal axial lengths from a middle zero axis = 15 is able to determine the distribution of primes in a given number space. This assumption finally bring us to the equation of Euler's identity.

Euler's identity is considered to be an exemplar of deep mathematical beauty as it shows a profound connection between the most fundamental numbers. Three (3) of the basic arithmetic operations occur exactly once each: ***addition***, ***multiplication***, and ***exponentiation*** _([Wikipedia](https://en.wikipedia.org/wiki/Euler%27s_identity))_.

Parallel Universes

Using these algorithms, the inflation structure of radial null geodesics spacetime for propagating light cone in primordial universe could be tabulated as below.

{{ site.github.latest_release.body }}

fully-expanded-incl-matrices

So we need to reformulate Einstein's general relativity in a language closer to that of the rest of fundamental physics, specifically Yang–Mills theory.

eQuantum Project
Copyright © 2023-2024

Reference:

Clone this wiki locally