Page 1 of 11
398
Advances inSocialSciencesResearchJournal –Vol.7, No.8 Publication Date: August 25, 2020
DOI:10.14738/assrj.77.8840
Yiping, Wang.(2020). ExploringGoldbach’s Conjecture, The Pebonacci Sequence And Its Five-Dimensional Vortex Structure
Based On The Logarithm Of The Circle. Advances in Social Sciences Research Journal, 7(8) 398-408
Exploring Goldbach’s Conjecture, The Pebonacci Sequence And
Its Five-Dimensional Vortex Structure Based On The Logarithm
Of The Circle
Wang Yiping
Association of ElderlyTechnologists,Quzhou City, Zhejiang Province, China
ABSTRACT
A method based on circle logarithm to prove Goldbach’s
conjecture and Pebonacci sequence is proposed. Its essence is to
deal with the real infinite series, each of the finite three
elements (prime numbers, number series) has asymmetry
problems, forming a basic even function one-variable quadratic
equation and odd function one-variable three- dimensional
number sequence; it is converted to "The irrelevant
mathematical model expands latently in a closed interval of 0
to 1," forming a five-dimensional vortex space structure. Keywords: Infinite sequence; latent infinity; logarithm of circle; cubic
equation in one variable; spatial structure of five-dimensional vortex;
THEFIBONACCISEQUENCEANDTHEONE-DIMENSIONALCUBICEQUATIONOFTHE
LOGARITHM OF THECIRCLE
The sequence of Fibonacci integersis
1,1,2,3,5,8,13,21,34,55,89,144,233,677,610,987,1597,2584;...
This sequence is famous because it has many fascinating properties. The most basic (actually
used to define them) property is that each item is the sum of the previous two items. For
example, 8=5+3,13=8+5,2584=1597+987,..., form a sequence of numbers in sequence, the combination of these three items is exactly the three-element asymmetric combination, and the center zero is at two Between an element and an element, and the central zero point
makes them achieve balance, conversion, and relative symmetry in linear superposition. The Fibonacci number sequence satisfies the condition: the central zero is introduced between
two elements and one element, so that each term is the sum of the previous binomial
(xa+xb)=(xc). The three-element combination{X}K(Z±3)≠{D}K(Z±3); the three-element
combination coefficient:1;3:3:1; Establish a cubic equation in one variable, (1.1) Ax
K(Z±3)±Bx
K(Z±2)+Cx
K(Z±1)±D=(1-η
2)K(Z±3){0,2}
K(Z±3){D0}
K(Z±3);
(1.2) (1-η∆
2)
(Z±3)=[{
K(Z±3)√D}/{D0}]K(Z±3);
Formula (1.1){D} is a cubic equation of one variable established under the condition of
continuous multiplication of three elements in each term of the Fibonacci number sequence. {D0}The
.
.
Page 2 of 11
URL: http://dx.doi.org/10.14738/assrj.78.8840 399
Advancesin Social SciencesResearch Journal(ASSRJ) Vol.7, Issue 8, August-2020
continuous average of the three elements of each term in the Fibonacci number sequence is the log
base of the circle.(1-η∆
2)
(Z±3) is a cubic equation of one variable established under the condition of
continuous multiplication of three elements in each term of the Fibonacci number sequence. The center zero point obtained by its solution satisfies: η∆=η∆a+(η∆b+η∆c)=1 and η∆a-(η∆b+η∆c)=0;;
the circle logarithm factor corresponds to { D0}. The value of each term of the Fibonacci number
sequence {R} is used in practical applications. Reflects {D0}≠{R}; there is a difference between the two:
(1.3) (1-η∆f2)
(Z±3)=[{R}-{D0})/{R}]
(Z±3);
(1.4) (1-ηf2)
(Z±3)= (1-η∆
2)
(Z±3)+ (1-η∆f2)
(Z±3);
The logarithm of the circle corresponding to the Fibonacci number order {R}
(1.5) (1-ηf2)
(Z±3)=[
{K(Z±3)√D}/{R}]K(Z±3);
The formula (1.5) (1-ηf2)
(Z±3) is the continuous multiplication of the Fibonacci number and the
change is [{K(Z±3)√D}/(1-η∆f2)]
(Z±3) Corresponding to{R}
(Z±3), establish the one-dimensional cubic
equation of the Fibonacci number sequence, which satisfies the synchronization of each item of the
Fibonacci number sequence and the power function factor. Based on the synchronization of the Fibonacci number order{R} and the logarithm of the circle (1- ηf2)
(Z±3), it is ensured that the power function integer is expanded to an infinite number order, using
natural numbers as the sequence, one by one corresponding to their number , Establish the
corresponding powerfunction. In this way, the Fibonacci number sequence corresponds to{10}K(Z)={10}K(Z±S±M±N±3)as the carrier, and q=(3) means that the three element conditions remain unchanged. Establish the Fibonacci
number sequence corresponding to the high-level counting method. Of course, it can also
correspond to other sequences or customize any secret sequence. It has the characteristics of both
openness and confidentiality. Such as natural numbers: properties(K=+1,0,-1)have integers, fractions, decimals and other
corresponding characteristicmodules and logarithms of circles.There are (Z) point infinity;(S)the
total number of digits of element natural numbers, M (area)sequence items; N (level)sequence
items (such as 1N={0→9} ; 2N={10→999} ; 3N=100→999} ; 4N={1000→9999} ;... :
Corresponding to the Fibonacci number sequence. Correspondence between natural numbers and Fibonacci numbers. For example, (2N+q)corresponds to (144→6765); (1N+q) to (0→89) corresponds to, and the corresponding
ending number q=(0,1→9,10). For example: each item {D} corresponds to{10}K(Z±S±M±N±q):
(K=+1)integer;(K=±1) corresponding number;(K=-1) score ; have
{0,1,2,3,4, 5, 6, 7, 8, 9, 10}K[(N=1)+q]/t, {11, 12, 13, 14, 15, 16, 17,18,19,20, 20 }K[(N=2)+q]/t...
(1,1,2, 3,5, 8,13,21,34,55,89), (144,233,677,610,987,1597,2584,2781,4181,6765)
5th sequence item(N=1)≈{10}
K(Z±S±M±(N=1)±(q=5){R}=8=5+3: {D}=8×5×3=120, 6th sequence item(N=1)≈{10}
K(Z±S±M±(N=1)±(q=5):{R}=13=8+5: {D}=13×8×5=5320,
Page 3 of 11
400
Yiping, W.(2020). Exploring Goldbach’s Conjecture, The Pebonacci Sequence And Its Five-Dimensional Vortex Structure Based On The Logarithm Of The
Circle. Advances in Social Sciences Research Journal, 7(8) 398-408. 18th sequence item(N=2)≈{10}
K(Z±S±M±(N=2,q=1)±(q=8):{R}=2584=1597+987;
{D}=2584×1597×987=403001576, Corresponding to the Fibonacci number sequence Topological circle logarithm:
(1-ηf2)
(Z±3)=[{
K(Z±3)√D}/{R}]K(Z±M±N±3)=∑(ji=3)(ηa+ηb+ηc)K(Z±N±3);
(1-η
2)
(Z±(N=5)±3)=
(K(Z±3)√120)K/[(1/3)K(8+5+3)]K(Z±1)≤1
(Z±(N=5)±3);
(1-η
2)
(Z±(N=6)±3)=
(K(Z±3)√5320)K/[(1/3)K(13+8+5)]K(Z±1)≤1)
(Z±(N=6)±3);
(1-η
2)
(Z±(N=18)±3)=
(K(Z±3)√403001576)K/[(1/3)K(2584+1597+987)]K(Z±(2N=10+8)±3)≤1
(Z±(N=18)±3;
Probabilistic circler logarithm
(1-ηH
2)K(Z±3)=[{Rji}/{2·R}]K(Z±3)=∑(ji=3)(ηa+ηb+ηc)K(Z±3)=1;
(1-η2)
(Z±(N=5)±3)=(8+5+3)/(2×16)=(ηa+ηb±ηc)=1;
(1-η2)
(Z±(N=6)±3)=(13+8+5)/(2×13)=(ηa+ηb±ηc)=1;
(1-η2)
(Z±(N=18)±3)=(2584+1597+987)/(2×2584)=(ηa+ηb±ηc)=1;
The logarithm of the limit circle of the center zero point:(ηa+ηb)±ηc=(0 or 1);
THEFIVE-DIMENSIONALSPACEDIAGRAMCODEOFTHEFIBONACCISEQUENCEANDTHE
CIRCLE LOGARITHM
Each of the three elements of the Fibonacci sequence corresponds to the third number, which is
connected into a two-dimensional spiral curve. This traditional description is infinite in the plane
space corresponding to the infinite Fibonacci number sequence. Traditional computer hardware
devices require switches with infinitely many crystal points. At present, discrete statistical
calculations are used, and entangled continuous multiplication elements cannot be accurately
processed. A multi-loop feedback system and optimization program software are used to
approximate calculations, and a huge computer structure is created. In order to reduce the structure
and increase the density of polycrystalline dots, the plane has 2nm lithography machining
technology, such as the famous AMSL lithography machine from Holland. The traditional multi-crystal point switch is a level layout for parallel operation of multiple
computers. Here, the plane layout is transformed into a multi-level three-dimensional space
structure. Specifically, using the Peibonacci number sequence as a model, a three-dimensional
vortex plus a precession five-dimensionalspace is established. The plan code is a logarithmic five- dimensionalspace code. The mathematical foundation of the structural form isthe cubic equation
in one variable. In the circle logarithm five-dimensional space map code, for any three elements, the logarithm of
the probability circle, the logarithm of the topological circle, and the logarithm of the center zero- point circle develop to a multi-level three-dimensionalspace.
Page 4 of 11
URL: http://dx.doi.org/10.14738/assrj.78.8840 401
Advancesin Social SciencesResearch Journal(ASSRJ) Vol.7, Issue 8, August-2020
Specific steps are as follows
Topologicallogarithmof circle (1-η2)
(Z±3/t=0 obtain (1-η2)
(Z±3/tandη=ηa+ηb=ηc=0 become rotation
Center of planehave
The length of the circumference of the center ellipse does not change. The long axis: [(1+η)
(Z±3)/t·{R}]
(Z±3)/t ; The short axis:[(1-η)
(Z±3)/t·{R}]
(Z±3)/t;
Or the length of the circumference is reduced:[(1-η2)
(Z±3/t{R}]
(Z±3/tthe perfect circle
Or the off-center distance of a perfect circle with constant circumference length: (η);
Orthe length ofthe off-center ellipse does not change (oval):off-center distance (η=ηa+ηb)
(1-η
2)
(Z±3){R}
K(Z±3)/t=[(1+ηa)
(Z±3)/t+(1+ηb)
(Z±3)/t]]{R}
K(Z±3)/t
Or (1-η2)
(Z±3)=[(1+ηa)
(Z±3/t(Y axis movement of the center ellipse)+(1+ηb)
(Z±3/t](Center ellipse X axis
movement]·{R}K(Z±3)/t
Probability logarithm of circle
(1-ηH
2)K(Z±3)={
K(Z±3)√D}/{R}]K(Z±3)=∑(i=3)(ηa+ηb+ηc)K(Z±3)={1}
K(Z±3);
Obtain(ηH)
(Z±3);Probabilityorangledistributionaccordingtothelevel(N=1,2,3,...sequence)onthe
rotating circularsurface, and synchronously distributed on the number axis precession curve. Combination: (A)+(B) in the equation result {0,2}K(Z±3)/t is two-dimensional rotation (the direction
of precession coincides with the direction of axis (straight line, curve tangent)) and three- dimensional direction Precession becomes a five-dimensional vortex space.That isto say, the five- dimensional vortex space develops the traditional two-dimensional infinite plane into an infinite
high-dimensional layered graphic description,reducing the floorspace and space of the plane. GOLDBACH'S CONJECTURE AND CIRCLE LOGARITHM FIVE-DIMENSIONAL SPACE GRAPH
CODE
Goldbach's conjecture has two types: strong and weak:
First, "the sum of two prime numbers that are large enough is even." Called Strong Goldbach
Conjecture. Current research progress: No one solves it in a satisfactory way. In 1967, the
mathematician Chen Jingrun proved that "the sum of the product of a sufficiently large prime
number and two prime numbers is an even number" Second, "the sum of three prime numbers large enough is even." Call the weak Goldbach conjecture. Current research progress: There is a proof by mathematician Tao Zexuan that the sum of five prime
numbers is even.Based on the proof of the central zero point {1/2}K(Z±S±M±N±p)/tof the Riemann
function and the results of the Fibonacci sequence, two Goldbach conjectures are derived and
proved. Based on the proof of the central zero point {1/2}K(Z±S±M±N±p)/t of the Riemann function and the
results of the Fibonacci sequence, two Goldbach conjectures are derived and proved. The connection between the quadratic equation in one variable and the strong Goldbach
conjecture
StrongGoldbach’s conjecture "any sufficiently large sumoftwo prime numbersis even",Suppose:
two arbitrarily large enough unknown two prime numbers for each term of infinite prime number
Page 5 of 11
402
Yiping, W.(2020). Exploring Goldbach’s Conjecture, The Pebonacci Sequence And Its Five-Dimensional Vortex Structure Based On The Logarithm Of The
Circle. Advances in Social Sciences Research Journal, 7(8) 398-408. {X}=x1,x2 item combination, introduce a known two prime number consecutive multiplication
auxiliary function to form each term two prime number consecutive multiplication
{D}=P1,P2, establish infinite each term "one-variable quadratic equation"; ∑(i=Z±S){X±D}K(Z±2)/t
Through the reciprocity and covariance of the logarithm of the circle, the two groups of each
uncertainty {X}=x1,x2 become the determination of relative symmetry. The central zero point
theorem(1-η2)K(Z±2)/t={0,1/2,1}K(Z±2)/tmakes these two asymmetric prime numbers
relatively symmetric
(2.1) (1-η)K(Z±2)/t{D0}
K(Z+2)/t=x1;(1+η)K(Z±2)/t{D0}
K(Z+2)/t=x2;
(2.2) {X}
K(Z+2)/t={0,2}
K(Z±2)/t{D0}
K(Z+2)/t
Proof
Suppose, two prime numbers are not known large enough {X}K(Z-2)/t=(x1,x2)K(Z-2)/t, two prime
numbers are known to be large enough {D}K(Z-2)/t=(P1P2)K(Z-2)/t
Sample module:
{X0}
K(1)/t={K(2)√X}={√(x1,x2)}
K(Z±S±M±N±2)/t;
{D0}
K(1)/t={(1/2)(P1,+P2)}
K(Z±S±M±N±1)/t;
(1-η2)K(Z±S±M±N±2)/t=[{X0}/{D0}]K(Z±S±M±N±2)/t
;
Suppose: two prime numbers are not known to be large enough {X}K(Z-2)/t=(x1,x2)K(Z-2)/t two prime
numbers are known to be large enough {D}K(Z-2)/t=(P1P2)K(Z-2)/tsample modulus: Based on symmetry
and association degeneration, directly select one of the two prime numbers, and the result remains
unchanged. Among them: power function K(Z±2)/t=K(Z±S±M±N±2)/trepresents the infinite expansion of the
two elements of infinite prime number; where: power function K(Z±S±M±N±2)/t means that the
two elements of an infinite prime number are multiplied infinitely;
Basedonsymmetry andassociativedegeneration, anytwo primenumbers aredirectlyselected, and
the result of the comparison remains unchanged.
;
{D0}
K(1)/t={Pc}
K(Z±S±M±N±1)/t;
Establish a quadratic equation in which each term of infinite elements is multiplied by two prime
numbers
(2.3) Ax
K(Z±S±M±N±2)/t±Bx
K(Z±S±M±N±1)/t+D=[x±√D]K(Z±S±M±N±2)/t = (1-η2)K(Z±2)/t{x0±D0}
K(Z±2)/t =(1-η2)K(Z±2/t{0 or 2}
K(Z±2)/t{D0}
K(Z)/t;
Represents the precession of the number axis of a quadratic equation in one element;
(2.4) {x0+D0}
K(Z±2)/t={2}
K(Z±2)/t;
Represents the rotation, balance, and mutation of a quadratic equation in one element. (2.5) {x0-D0}
K(Z±2)/t={0}
K(Z±2)/t ;
Page 6 of 11
URL: http://dx.doi.org/10.14738/assrj.78.8840 403
Advancesin Social SciencesResearch Journal(ASSRJ) Vol.7, Issue 8, August-2020
The original hypothesis {x0}≠{D0} through the relationship between the prime variable and the
auxiliary prime number, so that the prime number and the auxiliary prime number become an
equation, and the replacement becomes a prime number proof. {X}
K(Z±2)/t=x1,x2; {X}
K(Z±2)/t=(1-η2)K(Z±2)/t{D0}
K(Z±2)/t;
(2.6) (1-η
2)K(Z±2)/t{D0}
K(Z±2)/t=x1; (1+η)K(Z±2)/t{D0}
K(Z±2)/t=x2;
Relative symmetry
(2.7) η(1)+η(2)=1; η(2)·η(2)=1;η(2)-η(2)=0;
Covariance
(2.8) η(1)=η(2)=(1/2)+1=(2)
-1;
Center zero and even number theorem
(2.9) (1-η2)
-K(Z±S±M±N±2)/t={1/2}
+K(Z±S±M±N±2)/t and {2}
-K(Z±S±M±N±2)/t;
The result ofthe proofsatisfiesthe hypothesis of “the sumoftwo sufficiently large prime numbers”
for each term in an infinite number of prime numbers. Its central zero point is {0,1/2,1}K(Z-2)/t under
the condition of negative power function, which is called negative even number theorem; under
condition of positive power function, it is{0,2,1}K(Z+2)/t
,, This is called the even number theorem of
reciprocity;
(1-η
2)
-K(Z±S±M±N±2)/t={0,1/2,1}
K(Z-2)/t
(1-η
2)+K(Z±S±M±N±2)/t={0,2,1}
K(Z+2)/t={1}
K(Z+2)/t
In particular, under the condition of regularization, the normal symmetry distribution with the
antisymmetric combination coefficientC(Z±S+N+2)=C(Z±S-N-2) nmakes the original asymmetric
[X≠Pc]K(Z+2)/t, The relative symmetry and covariance are obtained through the logarithm of the
circle,and[X=Pc]K(Z±2)/tisobtained.Theoriginal auxiliarysettingfunction{Pc}K(Z+2)/tisequaltothe
unknown function {X}K(Z-2)/tThe reciprocity center zero of {Pc}K(Z±2)/t is established at all levels. In other words, the continuous multiplication of two unknown prime numbers is converted to
continuous addition, which proves the {{0,1/2,1}K(Z-2)/t of the sum of the two prime numbers and
the limit of the central zero point (critical line) =→{0,2,1}K(Z+2)/t,, becoming the limit of the sum of
two prime numbers corresponds to{Pc1+Pc2}K(Z±2)/t being an even number. which proves that there are two power functions: The sum of negative power prime numbers {x}
-1 ; (K=-1) and the central zero limit ( Critical
line) Even numbers with negative power {0,1/2,1}K(Z-2)/t; Prime numbers with positive power {x}
+1(K=+1) even numbers {0,2,1}K(Z+2)/t, becoming the
limit of the sum of two positive prime numbers corresponds to {Pc1+Pc2}K(Z±2)/t being an even
number.
Page 7 of 11
404
Yiping, W.(2020). Exploring Goldbach’s Conjecture, The Pebonacci Sequence And Its Five-Dimensional Vortex Structure Based On The Logarithm Of The
Circle. Advances in Social Sciences Research Journal, 7(8) 398-408. It is also proved that the "three unit {0,1} gauge invariance" of the logarithm of prime numbers and
the instability, inhomogeneity, and asymmetry of the distribution of prime numbers are
superimposed, making them relatively stable. , Uniformity, symmetry circle logarithm. The negative
power function that reliably and stably satisfies the central zero point and the limit is (1-η2)K(Z±S±M±N- 2)/t={1/2}K(Z-2)/tnegative odd Theorem, or the positive power function(1- η2)K(Z±S±M±N+2)/t={2}K(Z+2)/tthe positive couple theorem. Make the sum limit of the two prime numbers
of the positive power function composed of any sufficiently large positive power prime number
{2}K(Z±S±M±N±2)/teven number. Meet the strong Goldbach conjecture where{Pc1+Pc2}
K(Z±2)/t is even. The limit that becomes the sum of two positive prime numbers corresponds to {Pc1k+Pc2k}K(Z±2)/t
being the positive and negative even numbers of the positive and negative power prime numbers. The connection between the cubic equation in one variable and the weak Goldbach
conjecture. Weak Goldbach’s conjecture that "any sufficiently large sum of three prime numbers is aneven
number" also uses the above-mentioned mathematical technique of adding auxiliary functions to
three known prime number functionsto establish a cubic equation with infinite termorder, passing
the center of the circle logarithm Zero point processing,so that three prime numbers have a central
zero point, where one prime number is equal to the sum of the other two prime numbers. Suppose: Infinite prime number(Z) is composed of three unknown prime numbers with arbitrarily
large asymmetry, multiplied by{X}K(Z±3)/t, and three known auxiliary functions are introduced
Multiplying any sufficiently large asymmetry ofthree prime numbers {D}K(Z±3)/t
{X}
K(Z-3)/t=∑(j=(Z±S±M±N±3)∏(p=3)(xaxbxC)
-1
;
{D}
K(Z±3)/t=∑(j=(Z±S±M±N±3)∏(p=3)(PaPbPC)+1;
Three different prime numbers Pa≤ Pb≤ Pc;
Pc is the largestprime number;
Model(K(Z+3)√(xaxbxC))K(Z-1)/tand[(1/3)
-1(xa
-1+xb
-1+xC
-1)]K(Z-1)/t
Arithmetic average of three prime numbers:
{X0}
K(Z-3)/t=∑(j=(Z±S±M±N±3)(1/C(Z±S±M±N±3))
k∏(p=3)(xaxbxC)
-1;
{D0}
K(Z+3)/t=∑(j=(Z±S±M±N±3)(1/C(Z±S±M±N±3))
k∏(p=3)(DaDbDC)+1;
The logarithm of the circle of the cubic equation multiplied by three prime numbers
(1-η∆
2)K(Z±3)/t= {X0}/{D0}
K(Z±3)/t;
Directly use three prime numbers and add the logarithm of the circle with the base of the major
prime number {PC}
(1-ηP
2)K(Z±3)/t= {X0}/{Pc}
K(Z±3)/t;
The "binomial" that constitutes a multivariate cubic equation of one variable{X±(K(Z±3)√D)}K(Z±3)/t
Through the reciprocity and covariance of the circle logarithm theorem, they become relative
symmetry, the center zero is in three prime numbers[(1/3)
-1(xa
-1+xb
-1+xC
-1)]K(Z-1)/t Between (Z-1)/t, the relative symmetry(xa+xb)=xC issatisfied; if you directly choose (Pa+Pb)=PC, it will not affect the
relativity of the circle logarithm. (3.1) Ax
K(Z±S±M±N±3)/t±Bx
K(Z±S±M±N±2)/t+Cx
K(Z±S±M±N±1)/t±D=[x±√D]K(Z±S±M±N±2)/t
Page 8 of 11
URL: http://dx.doi.org/10.14738/assrj.78.8840 405
Advancesin Social SciencesResearch Journal(ASSRJ) Vol.7, Issue 8, August-2020 = (1-η∆
2)K(Z±3)/t[x0±D0]K(Z±3)/t =(1-η∆
2)K(Z±3/t{0 or 2}
K(Z±3)/t{D0}
K(Z±3)/t;
Three prime numbers for the asymmetry of multiplication
(3.2) 0≤(1-η∆
2)K(Z±3)/t≤1;
Among them:
The precession of the cubic equation in one variable;
(3.3) [x0+D0]K(Z±3)/t={2}
K(Z±3)/t
Rotation, balance and sudden change of cubic equation in one variable. (3.4) [x0-D0]K(Z±3)/t={0}
K(Z±3)/t
When directly using the largest prime number{PC}K(Z+3)/tamong the three prime numbers, because
{D0}K(Z+3)/tisnotequalto{PC}K(Z+3)/t,itisalsoThatistosay,thearithmeticaverageofprimenumbers
ofthe cubic equation {PC}K(Z+3)/tt is not equal to the three direct prime numbers, there is an error of
{D0}K(Z+3)/t, and the logarithm through the error circle (1-η∆f2)
(Z±3) processing, (3.5) (1-η∆f2)K(Z+3)/t=[{PC}-{D0})/{PC}]K(Z+3)/t
(3.6) (1-ηp
2)K(Z+3)/t= (1-η∆
2)K(Z+3)/t+(1-η∆f2)K(Z+3)/t
Among the three prime numbers, the largest prime number is the characteristic modulus value
{PC}
(Z±3) corresponding to the circle logarithm (1-ηp
2)
(Z±3)
(3.7) (1-ηp
2)
(Z±3)/t=[{
K(Z±3)√D}/{PC}]K(Z±3)/t;
(3.8) (1-ηp
2)K(Z±3)/t={X0}/{PC}
K(Z±3)/t;
(3.9) {X}
K(Z-3)/t=(1-ηp
2)K(Z±S±M±N±3)/t{PC}
K(Z±S±M±N±3)/t
;
Relative symmetry
(3.10) (η(a)+η(b))+η(c)=1 or (η(a)+η(b))-η(c)=0;
Covariance
(3.11) (η(a)+η(b))=η(c)=(1/2);
The even number theorem for the reciprocity of the center zero point;
(3.12) (1-ηp
2)
-K(Z±S±M±N±3)/t={0,1/2,1}
+K(Z±S±M±N±3)/tand{0,2,1}
-K(Z±S±M±N±3)/t;
Solve three prime numbersin line with the three prime numbersintroduced by the auxiliary
(3.13) Pa=(1-ηa2)K(Z±3)/t(1-ηp
2)K(Z±3)/t{PC}
K(Z±3)/t;
Pb=(1-ηb2)K(Z±3)/t(1-ηp
2)K(Z±3)/t{PC}
K(Z±3)/t;
Pc=(1-ηc2)K(Z±3)/t(1-ηp
2)K(Z±3)/t{PC}
K(Z±3)/t;
the formula (3.1)-3.13) prove that the reciprocal {X}
k and {PC}K three prime numbers
correspond to the central zero point of the extreme positive and negative power primenumbers, {1/2}K(Z-3)/t=→{2}K(Z+3)/t. Have arbitrarily large enough three even numbers with positive powers
and even numbers with negative powers. On the contrary, this algorithm also holds. Make the limit of the sum of the three prime numbers of a positive power function composed of any
sufficiently large positive power prime number {2}K(Z±S±M±N±3)/t even number.It has been proved that
t{hPe "three unit {0,1} gauge invariance" of prime number circle logarithms and the stable circle C}K=PaK+PbK+PcK;
Page 9 of 11
406
Yiping, W.(2020). Exploring Goldbach’s Conjecture, The Pebonacci Sequence And Its Five-Dimensional Vortex Structure Based On The Logarithm Of The
Circle. Advances in Social Sciences Research Journal, 7(8) 398-408. logarithmic factors of the instability, inhomogeneity and asymmetry of prime number distribution
are superimposed, making them relatively stable , Uniformity, symmetry circle logarithm. The
negative power function that reliably and stably satisfies the central zero point and the limit is (1- η2)K(Z±S±M±N-3)/t={1/2}K(Z-3)/tnegative power The even number theorem, or positive power
function(1-η2)K(Z±S±M±N+3)/t={2}K(Z±3)/tpositive power even number theorem.Meet the strong
Goldbach conjecture where {Pa+Pbk+Pck}K(Z±3)/t is even. The relationship between Goldbach's conjecture and the five-dimensional space graph code
of circle logarithm
Description of Goldbach’s conjecture: any sufficiently large unknown two, three..., S prime number
functions are successively multiplied for each term {X}K(Z-p)/t, and the corresponding known prime
number{Pc}K(Z+p)/t, which can form each term of the "one-variable two, three, ..., binomial equation
of S degree. It becomes {X}
K(Z-p)/t≠{D}
K(Z+p)/tor {X}
K(Z-p)/t≠{Pc}
K(Z+p)/t Through circular logarithm
processing, it is converted into two prime number functions of relative symmetry by means of the
average value of the prime number function. The covariance of prime elements becomes
{X}
K(Z-p)/t≈{D}
K(Z+p)/t or {X}
K(Z-p)/t≈{Pc}
K(Z+p)/t. " ≈ " means equivalent conversion. (4.1) {
K(Z±S)√Pc}
K(Z±S±M±N±p)/t=(1-η2)
- K(Z±S±M±N±p)/t{0,2}
K(Z±S±M±N±p)/t{Pc}
K(Z±S±M±N±p)/t;
(4.2) (1-η
2)K(Z±S±M±N±p)/t={0,1/2,1}
K(Z±S±M±N±p)/t;
Formula: (4.1)-(4.2), {{0 or 1}K(Z±S±M±N±p)/tis the boundary of the prime number combination
level,{1/2}K(Z±S±M±N±p)/tis the central zero point of each level of each item, balance, sudden change, positive and negative power even number theorem. Prime eigenmode
(4.3) {P0}
K(Z±S±M±N±p)/t=(1-ηp
2)K(Z±S±M±N±p)/t{5}
K(Z±S±M±N±p)/t
(4.4) 0≤(1-ηp
2)K(Z±S±M±N±p)/t≤{1};
In formula (4.4),{1}is the probability distribution; {0 to 1}K(Z±S±M±N±p)/t is the topology status;
Under the conditions of prime number characteristic modulus invariance and circle logarithm
invariance, the power function reflects that prime numbers can be calculated for infinite series
between [0,1]. Among them, the combination of prime numbers is generally used as the
characteristic modulus of the equation (the average value of the positive, medium, and negative
power functions). If the prime number is directly used as the characteristic modulus{Pc}, the logarithm of the error
circle between the prime number{Pc} and the prime number average {P0}(1-ηf2)K(Z±S±M±N±p)/tmust
be processed first , And the logarithm of the stability circle of the prime number distribution
(1-η∆f2)K(Z+3)/t=[{PC}-{D0})/{PC}]K(Z+3)/t, in order to accurately calculate and produce digital and
graphic codes. In the infinite prime number graph, the center zero point is the rotation of the plane center, and the
center zero points are connected by the number axis.In the traditional two-dimensional drawing of
code and digital, the plane is infinite, and the three-dimensional five-dimensional space is formed
by using the circle logarithm and the hierarchical structure. Similar to the method of the natural
number sequence corresponding to the Fibonacci sequence, the graphic code and digital program
design are carriedout. CONCLUSION
Page 10 of 11
URL: http://dx.doi.org/10.14738/assrj.78.8840 407
Advancesin Social SciencesResearch Journal(ASSRJ) Vol.7, Issue 8, August-2020
There are many "natural or man-made" rules for infinite natural numbers, which form an ordered
or unordered sequence of each item. Goldbach ’ s conjecture and the Pebonacci sequence are just
some of the representative and famous sequences. "Each item" can form a closed "algebra- geometry" any finite one-element N-th degree calculus polynomial, and the nested nature of its
composition forms asequence
The circle logarithm algorithm reflects the combination of prime numbers with reciprocity, covariance,numericalprobability,andcharacteristicmodesofisomorphictopology(averagevalues
ofpositive,medium, andinverse functions)that canbemutuallyconverted.Once theyare converted
into calculus polynomial equations and converted to circle logarithms, the number domain sets are
controlled to be in infinite discrete characteristic modes, and the latent infinity expansion between
[0 to 1] can be controlled by the circle logarithm. The completeness and continuity, discreteness
and continuity are unified into a whole, and a simple formula is used to describe the five- dimensional structure of their vortex and precession. (5.1) W=(1-η
2)K(Z)/t{0,2}
K(Z)/tW0;
(5.2) Wi=[(1-ηhi2)(1-η
2)]K(Z)/tW0; 0≤(1-η2)K(Z)/t≤1;
Reciprocity theorem:
(5.3) (1-η
2)
-K(Z)/t·(1-η
2)+K(Z)/t=1 and (1-ηhi2)K(Z)/t+(1-η
2)K(Z)/t=1;
Probability Circle Logarithm Theorem:
(5.4) (1-ηH
2)K(Z)/t=∑(i=S)(1-ηhi2)K(Z-S)/t={0 or1}K(Z)/t;
Topological circle logarithm theorem:
(5.5) (1-η2)K(Z)/t=∑(i=S)(1-ηi2)K(Z±S)/t={0 to1}K(Z)/t;
Central symmetry zero point and logarithm theorem of even circle:
(5.6) (1-η
2)K(Z)/t={0,1/2,1}
K(Z-S)/t={0,2,1}
K(Z+S)/t;
The circle logarithm algorithm describes symmetry and asymmetry, unit stability, probability, topology, randomness, fractal, chaos, parallel/serial, dynamic system, and combines the discrete
and entangled types into a whole based on the central zero theorem. On the basis of the invariable
characteristic modulus W0 and the invariant circle logarithm(1-η2), the independent mathematical
model is realized in the {0 to 1} closed area, and the arithmetic calculation of the power function
sequence is carried out. It has self-consistent, concise, unified, beautiful, powerful and applicable
computing vitality. References
[1] , John Stacher, "Einstein's Miracle Year-Five Papers that Changed the Face of Physics", translated by Fan Dainian
and others, Shanghai Science and Technology Education Press, November 2001
Page 11 of 11
408
Yiping, W.(2020). Exploring Goldbach’s Conjecture, The Pebonacci Sequence And Its Five-Dimensional Vortex Structure Based On The Logarithm Of The
Circle. Advances in Social Sciences Research Journal, 7(8) 398-408. [2] , [America] M. Klein, Deng Donggao, etc. Translated "Ancient and Modern Mathematical Thoughts" (Volumes 1, 2
and 3) Shanghai Science and Technology Press August 2014
[3] , "Langlands Program", "100 Scientific Problems in the 21st Century" p793-p798 Jilin People's Publishing House, January 2000
[4] , Xu Lizhi "Selected Lectures on Mathematical Methodology" p47-p101 Huazhong Institute of Technology Press, April 1983 first edition
[5] , Xu Lizhi, "Berkeley's Paradox and the Concept of Pointwise Continuity and Related Issues", "Research in Advanced
Mathematics," 2013 No. 5P33-35
[6] , [ fi ] E AMaor, translated by Zhou Changzhi and others, "e: The Storg of Number" People's Posts and
Telecommunications Press, October 2011
[7] , [America] M·Livio, Translated by Huang Zheng "Meditations on Mathematics", Beijing People's Posts and
Telecommunications Press, September 2011
[8] , Wang Yiping "NP-P and the Structure of Relativity" [America] "Journal of Mathematics and Statistical
Sciences" ((JCCM) 2018/9 p1-14 September 2018 edition
[9] , Wang Yiping, "Exploring the Scientific Philosophy and Application of Langlands Program", "International Journal
of Advanced Research" (ILAR) 2020/1 p466-500 January 2020 edition
[10] , Wang Yiping, "The Road to Calculus Reform? "International Journal of Advanced Studies" (ILAR) 2020/1 p466- 500 April 2020 edition