By Zhou M (2022).
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Greener Journal of
Applied Mathematics and Statistics Vol. 2(1), pp. 6-7, 2022 Copyright ©2022, the
copyright of this article is retained by the author(s) http://gjournals.org/GJAMS |
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All even numbers can expressed as a prime
minus a prime
Suqian Economy
and Trade vocational School
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ARTICLE INFO |
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Article
No.: 122821161 Type: Short Comm. |
Accepted: 10/12/2021 Published: 31/12/2021 |
*Corresponding
Author Zhou Mi E-mail: zhoumi19920626@ 163.com |
Keywords:
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INTRODUCTION
A
man found that all even numbers can expressed as a prime minus a prime, and
this conjecture is still not solved, I found a way to solve it.
MAIN DERIVATIONS
Let
us look at a matrix: in 1934, one ground breaking mathematician from the
Indian/ Bangladesh region Harish Chandra (1923–1983), in the field of number
theory, has made a founding contribution of harmonic analysis on semi simple
Lie groups. This subject is equally important for an engineer, as a synthesis
of Fourier analysis, special functions and invariant theory etc., and it has
also become a basic tool in analytic number theory, via the theory of automorphic forms, leading to Langlands program eventually. It became one of the
major mathematical edifices of the second half of the twentieth century [9].
Chandra matrix is a square sieve, where the first row of the square sieve
consists of the first element of 4, the difference between next every two
adjacent numbers is 3, forms an arithmetic sequence:
4,7,10, ... The first column equals to the first row.
The second row, third row, ...... any subsequent rows are also arithmetic
sequence, but the difference between two adjacent numbers gradually become
larger, and they are 5,7,9,11,13, ... respectively, and they are all odd
numbers, and the matrix is symmetrical, as shown below with modulo equivalent
representation:
4
7 10 13 16 19 22 25 ……
1
7 12 17 22 27 32 37 42 ……
2
10 17 24 31 38 45 52 59 ……
3
13 22 31 40 49 58 67 76 ……
4
16 27 38 49 60 71 82 93 ……
5
19 32 45 58 71 84 97 110 ……
.............
The
secret of this square sieve is: If a natural number N appear in the table, then
2N+1 certainly is not a prime number, because 2 times of remaining plus 1 is at
least one of the divisors in the above modulo operations. If N does not appear
in the table, then 2N+1 is definitely a prime number, because 2 times of
remaining plus 1 is not any of the divisor in the
above modulo operation. Primes are left out. Almost all primes can be launched
from this table, assume that the number of primes follow the prime number
theorem x/ln(x) in arithmetical range of the numbers.
Click here to download Manuscript: 1-1.pdf Click here to view linked References
Based on above observations, we made a few similar matrices accordingly
(lifting by x):
4+x 7+x 10+x 13+x……
7+x 12+x 17+x 22+x…….
10+x 17+x 24+x 31+x……
……
Lifting
by any positive integer can be obtained if the natural number N in the matrix,
2*N-(2x-1) is certainly not a prime number, if not 2*N-(2x-1) must be a prime
number. If a number N is not in the matrix beginning with 4 and 4+x,then
2N+1and 2N-(2x-1) are primes. If so,(2N+1)-(2N-(2x-1))=prime-prime=2x,x
is all numbers, so 2x is all even numbers! Now, we have to found the N which
not in the two matrixes. All the numbers not in the matrix of 4,and if these numbers all appear in the matrix of 4+x,is not
set up. Because Numbers in 4 and not in 4. is all
numbers, now we assume not in 4 is equally within 4+x,so numbers in 4 and
numbers in 4+x are all numbers, obviously is not set up! Exist N not in the two
matrix! We can get a conclusion: all even numbers can possibly expressed as a
prime minus a prime
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Cite this Article: Zhou M (2022). |