Chapter 1: Matrix Online Characteristic Number and Goldbach’s Conjecture Baoshan Zhang 1 (School of Mathematics and Statistics, Nanjing Audit University, Nanjing, China , Zip code: 211815) Email:
[email protected],
[email protected] Abstract:In this paper, it is determined by the consecutive odd numbers between 3 to 2n +1, and study to the intrinsic properties of a class of matrix sequence {}An . Through the establishment of matrix online number concept, characteristics and the online number column use mathematical induction to prove the some properties of this kind of matrix on the number of online features (Theorem 1). Finally, it is given a trial to prove the Goldbach’s conjecture (Theorem 6). This is the author in the years to explore prime properties in the process of research and discovery, and believe that this finding is of great significance. Keywords Prime numbers;Online character; Online characteristic columns; Goldbach's conjecture. Classification:O15.156 MSC:11A41 §1 Introduction Goldbach 's Conjecture is one of the three Difficult mathematical problems in modern world, It was first found in teaching by C.Goldbach(1690-1764), who was the German high school teachers [1~3]. On June 7, 1742 , Goldbach write to the great mathematician Euler (1707~1783), and asked that his experiments have found. Euler said to Goldbach in a reply letter, that he believes that the conclusion is correct, but he can't prove. And then Euler confirmed the following two guess [1~8]: (1) Strong Goldbach's Conjecture: any more than 4 even can be always expressed as the sum of the two odd primes.