Greener Journal of Science, Engineering and Technological Research. 

Vol. 5 (2), pp. 33-36, September 2015.

ISSN: 2276-7835

 

 

Short Comm.

 

Manuscript Number: 072415103

 

 

Lifting Chandra Matrix to Solve Goldbach Conjecture

 

Mi Zhou¹, Steed Huang*²

 

1Huaiyin Institute of Technology, Jiangsu, China. Email: zhoumi19920626@ 163. com

29920 Pacific Heights BLVD, San Diego, CA 92121, USA.

 

*Corresponding Author’s Email: junh @ sqc.edu.cn

 

ABSTRACT

 

This paper hints a very simple method of lifting Chandra matrices to solve Goldbach conjecture, by lifting we mean to add a positive integer to every element of the matrix, this way we constructed a set of Chandra matrices, which are equivalent to a progressive modulo operations until any large number, for judging if the number is a prime or not. The advantage of this method is that it offers a quick and an easy understandable way for any prime number verification or partition. The disadvantage of this method is that both the number of matrices and the dimension of each matrix are infinite. In this paper, we show that all positive even integers n ≥ 40 can be expressed as the sum of two primes, those n < 40 are trivial cases.

 

Keywords: Chandra matrix; Goldbach conjecture; Prime numbers

 

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REFERENCES

 

[1]  Eric W. Weisstein, "Goldbach Number", MathWorld; http://mathworld.wolfram.com/GoldbachNumber.html

 

[2]  Tomás Oliveira e Silva, "Goldbach conjecture verification", http://sweet.ua.pt/tos/goldbach.html

 

[3]    Jeff Law, "The Circle Method on the Binary Goldbach Conjecture", 36 Pages Report, Mathematics Department, Princeton University, April 3, 2005.

 

[4]  Jingrun Chen, "On the representation of a large even integer as the sum of a prime and the product of at most two primes". Kexue Tongbao 11 (9): 385–386, 1966.

 

[5]  Henry F. Fliegel; Douglas S. Robertson, "Goldbach's Comet: the numbers related to Goldbach's Conjecture”, Journal of Recreational Mathematics, v21(1) 1-7, 1989.

 

[6]  Roger Ellman, A PROOF OF "GOLDBACH'S CONJECTURE", May 10, 2000, Roger Ellman, 320 Gemma Circle, Santa Rosa, CA 95404, USA.

 

[7]   Subhash Kak, Goldbach Partitions and Sequences, Resonance, Volume 19, Issue 11, pp 1028-1037, November 2014.

 

[8]  Roger Howe, “A Biographical Memoir for Harish Chandra”, National Academy of Sciences, 2011.

 

 

Cite this Article: Zhou M; Huang S (2015). Lifting Chandra Matrix to Solve Goldbach Conjecture. Greener Journal of Science Engineering and Technological Research, 5 (2): 26-32, http://doi.org/10.15580/GJSETR.2015.2.072415103.