A large even integer number can be expressed as the sum of two prime numbers
The proof of the Goldbach conjecture is based on Chen Jingrun's theorem and negative space
Jianhua Li, Feng, Xie , Lee Xie Li, Ganquan Xie
Dayuling Supercomputing Science Center, CHINA
Wangcheng, Changsha, Hunan, China
GL GEOPHYSICAL LSBORATORY, USA
August 16, 2025
Abstract
Chen Jingrun proved that a large even integer number X can be expressed as
1. X = p + p1
or
2. X = p + p2 p3
Here p, p1, p2 , p 3 are prime numbers.
By negative space theory, the second option is excluded. We proved that a large even integer number can be expressed as the sum of two prime numbers .
Intrduction
Chen Jingrun's paper is a monument to Chinese mathematics in the world. He brought the sieve method to its pinnacle of glory.
Chen Jingrun, a true survivor of the Cultural Revolution, completed his proof in January 1966. Professor Min Sihe reviewed it and found no flaws. Pan Chengdong also reviewed it and found no flaws. Professor Guan Zhaozhi, an expert in functional analysis, Wu Wenjun, a topology expert, and Professor Min, a number theory expert, and Professor Min Sihe, a functional theory expert, jointly recommended it for publication in Volume 17 of the Chinese Science Bulletin in September 1966. In 1973, the full text of Chen's theorem was published in Chinese Science. From 1973 to his death in 1996, Chen Jingrun worked for another 23 years. He tried every possible way to eliminate his second option possibility: a large even numbers = p + p2 p3. This left only option 1, large even numbers = p + p1, where p, p1, p2 , p 3 are prime numbers. if so, the Goldbach conjecture was proved. However, he tried every possible way to improve the sieve method, but are all fail. He didn't know about negative space. He also didn't know that this was a problem that couldn't be proved in positive space. Chen Jingrun's extreme efforts could only prove
1 + 2.
Proof of GoldBach conjecture
Based on Chen Jingrun's theorem and the theory of Negative Space, we can prove that if there is option 2,
X = p +p2 p3 , (1)
then the option 1 must exist.
X = p +p1, (2)
Is hold. Goldbach conjecture is proved.
A large even integer number can be expressed as the sum of two prime numbers.
Thus, the 283-year-old puzzle was solved.
Positive Space And Negative Space And Invisible Science
Jianhua Li, Feng Xie, Lee Xie and Ganquan Xie
1 Dayuling Super Science Center, Wang Chen, Changsha, Hunan, China
2 GL Geophysical Laboratory, USA
Like in the situation where there was no previous imaginary number i =√(1) , , we can not solve equation x2+1=0.
What happens, if science did not accept imaginary number i=√(-1) ?
The same thing is happening: Invisible science problems cannot be solved if science does not accept "Positive Space and Negative Space".
We ask question : in polar coordinates of a two-dimensional plane, (ρ,θ),ρ≥0, is a point in the plane; for the same θ, where is (-ρ,θ) ? This question can interest students from middle school to university. This topic concerns professors and scientists at all levels. In this paper, we propose positive space and negative space and invisible science .
Let ( x,y,z) be a point in 3D space, r = ±√( x2+y 2+z 2), the r =+√( x2+y 2+z 2), used only as the radius of the point
( r, θ, φ ) of the 3D spherical coordinates in sciences previously. In 3D spherical coordinate, the set of the points
( r, θ, φ ) with positive radial coordinate,r ≥0, 0≤r≤+∞ , called to be 3D positive space, the conventional three dimensional space we inhabit. For same ( θ, φ ) of the points in the positive space, no point ( -r, θ, φ ) exists in conventional three dimensional positive space. Thus, we propose a negative space, we now select the r =-√( x2+y 2+z 2), a new negative space is defined as the set of these points (- r, θ, φ ). In 3D spherical coordinate, the set of the points, (- r, θ, φ ),with negative radial coordinate, -∞ <r≤-0, is defined to be the 3D negative space.The origin +0 of positive space can be an arbitrary location. For a given 3D sphere coordinate in positive space, point, ( r, θ, φ ),in the positive space and point, ( -r, θ, φ ), in negative space are defined as corresponding points with the same latitude and longitude ( θ, φ ). The origin +0 of the positive space and the origin -0 of the negative space are corresponding points, but distinct points. The 3D negative space is corresponding space of the 3D positive space.
By 3D geometry knowledge, every sphere surface is a 2D double-sided curve surface or bilateral curve surface. The positive space lies on the outside lateral of the spherical surface, with the normal directed outward and with a positive radial coordinate ; the radius from the positive origin to the point is positive. The negative space lies on the inside lateral of the spherical surface, with the normal directed inward and with negative radial coordinate , the radius from the negative origin to the point is negative. The 3D positive space and negative spaces are not connected. The negative space and the positive space have no intersection. The negative space and the positive space are Euclid geometry space, Gravity, acoustic, elastic and electromagnetic equations and science hold true in positive space and negative Space.
The debate on negative space theory resembles arguments over the scientific merit of Copernicus, Newton, Maxwell, and Einstein's initial publications.
Please read "Based on negative space theory, an advanced GLHUA cloak discovered in [22] can be made from ordinary materials with a finite refractive index greater than one without metamaterials. Creating and product producing completely perfectly GLHUA invisible cloaks is not a myth but a practical task for the next step."
" The G sphere can be understood scientifically, and the negative space that induces it can also be understood scientifically. Negative space theory has been confirmed by the invisible G sphere and invisible science. Positive space science is global visible, scattering science and can be local invisible; Nnegative space science is global invisible, nonscattering science, can be local visible.
" The Simulations confirm the perfect invisibility of the G sphere and the GLHUA cloak without infinite speed violation, without exceeding the speed of light and without time delay, overcoming the infinite phase velocity violation and superluminal propagation fundamental problems in Pendry's cloak (2006, [4], Science 312, 1125907) and the time delay imperfect invisibility problem in Ulf's cloak (2009 [7], Science 323, 110; 2011 [8])
------------------------------
Ganquan Xie Jianhua Li
Professor
Dayuling Super Science Center
Wang Chen Changsha China
https://www.zhihu.com/question/66793557/answer/262054935
GL Geophysical Laboratory, USA
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In case you need to reference your post, it will be below:
Dear Professor Marietta Damond and every professor,
Physics, Mathematics, Social Sciences, Thinking Psychology, and Health Sciences unite to reseach and discuss
Positive Space and Negative Space and Invisible Science
I am Ganquan Xie, I have created my BIO in
https://members.aaas.org/profile?UserKey=3b210144-beac-44be-b285-0196f22040bd
Primary Scientific Discipline
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Yrs of Work Experience in Current Field
Ganq Xie and Jianh Li received Chinese Scientific Congress Award 1978 on 3DFEM in 1972
Chinese Scientific Congress
1978
GL Geo[physicall Laboratory Software Best 0f 2019 Berkeley
CA Berkeley Award
2019
Lax wrote "He (Xie) is very knowledgeable and inventive scientist with exellent phys,math, num,
lax@courant.nyu.edu
2001
P.D.LLax praize "XIe is a very effective user of the computer, he is a demon for hard work"
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1 to 5 of 12 total
Posted By ganquan xie 08-04-2025 10:17 AM
Found In Library: Physics (Section B)
Posted By ganquan xie 08-04-2025 10:17 AM
Found In Egroup: Physics (Section B) \ view thread
Positive Space And Negative Space And Invisible Science Jianhua Li, Feng Xie, Lee Xie and Ganquan Xie 1 Dayuling Super Science Center, Wang Chen, Changsha, Hunan, China 2 GL Geophysical Laboratory, USA Like in the situation where there was no previous imaginary number i =√(1) , , ...
Posted By ganquan xie 08-04-2025 10:07 AM
Found In Egroup: Social, Economic, and Political Sciences (Section K) \ view thread
Positive Space And Negative Space And Invisible Science Jianhua Li, Feng Xie, Lee Xie and Ganquan Xie 1 Dayuling Super Science Center, Wang Chen, Changsha, Hunan, China 2 GL Geophysical Laboratory, USA Like in the situation where there was no previous imaginary number i =√(1) , , we can not solve ...
Posted By ganquan xie 08-04-2025 10:06 AM
Found In Library: Social, Economic, and Political Sciences (Section K)
Posted By ganquan xie 08-04-2025 09:59 AM
Found In Library: Mathematics (Section A)
Like in the situation where there was no previous imaginary number i =√(1) , we can not solve equation x2+1=0 , What happens, if science did not accept imaginary number,i =√(1)? The same thing is happening: Invisible science problems cannot be solved if science does not accept "Positive Space and ...
Posted By ganquan xie 08-04-2025 09:59 AM
Found In Egroup: Mathematics (Section A) \ view thread
Positive Space And Negative Space And Invisible Science Jianhua Li, Feng Xie, Lee Xie and Ganquan Xie 1 Dayuling Super Science Center, Wang Chen, Changsha, Hunan, China 2 GL Geophysical Laboratory, USA Like in the situation where there was no previous imaginary number i =√(1) , , ...
Posted By ganquan xie 08-03-2025 10:27 PM
Found In Library: Physics (Section B)
Posted By ganquan xie 08-03-2025 10:27 PM
Found In Egroup: Physics (Section B) \ view thread
Positive Space And Negative Space And Invisible Science Jianhua Li, Feng Xie, Lee Xie and Ganquan Xie 1 Dayuling Super Science Center, Wang Chen, Changsha, Hunan, China 2 GL Geophysical Laboratory, USA Like in the situation where there was no previous imaginary number i =√(1) , , ...
Posted By ganquan xie 08-03-2025 05:20 PM
Found In Egroup: Physics (Section B) \ view thread
Positive Space And Negative Space And Invisible Science Jianhua Li, Feng Xie, Lee Xie and Ganquan Xie 1 Dayuling Super Science Center, Wang Chen, Changsha, Hunan, China 2 GL Geophysical Laboratory, USA Like in the situation where there was no previous imaginary number i =√(1)
Posted By ganquan xie 08-03-2025 05:19 PM
Found In Library: Physics (Section B)
Positive Space And Negive Space and Invisible Science is imporant new physics. The debate on negative space theory resembles arguments over the scientific merit of Copernicus, Newton, Maxwell, and Einstein's initial publications. Please read "Based on negative space theory, an advanced GLHUA cloak discovered ...
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Sincerely
Ganquan Xie
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