The Equivalent of the Goldbach Conjecture and "Even Number Is the Difference Between Two Prime Numbers"
Volume 7, Issue 3, June 2019, Pages: 161-164
Received: Apr. 9, 2019;
Published: Jun. 15, 2019
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Mi Zhou, Philosophy Department, Ren Min University of China, Beijing, China; Commerce Department, Suqian Economic and Trade Vocational School, Suqian, China
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Goldbach conjecture can be described as "an even number is the sum of two prime Numbers,", this description is well known, the Canadian guy's book «the unresolved problems in number theory», put forward a conjecture which is contrary to goldbach: that "evens are the different between two prime Numbers", the difficulty of the conjecture is not less than goldbach conjecture, as also an unresolved problem.This paper, based on the promotion of chandra symmetric matrix, there is a natural number as long as there is any matrix at the same time don't appear in the matrix as well as the matrix beginning of 4 , thus making the conjecture set up, thus obtained the equivalent propositions of "an even number are the difference between the two primes" conjecture: 2mn + m + n and 2m + m+n + x (m, n for any natural number, x takes only one value at a time, is a fixed) Is these two formulas can show all the natural Numbers greater than 4 + x? If not, then the "even number is the difference between two prime Numbers" conjecture is true, which is the equivalent of the conjecture. And I get the equivalent proposition of golabach too! Mathematicians can turn to this description, as long as have the solution of this new description, the original conjecture will also be solved, the road of research also greatly broaden, mathematicians on the new description of the solution, in the process of research should be have some achievements.The difference between this equivalent proposition and the original conjecture is that the original conjecture is only a description of a concept, while the equivalent proposition tends to be digitized and formulated.
Number Theory, Equivalent Proposition, Chandra Matrix
To cite this article
The Equivalent of the Goldbach Conjecture and "Even Number Is the Difference Between Two Prime Numbers", Science Discovery.
Vol. 7, No. 3,
2019, pp. 161-164.