Goldbach's conjecture and the ring of integers

Goldbach's conjecture and the ring of integers

​ “哥德巴赫猜想：每一个大于2All even numbers can be written as the sum of two prime numbers.

​ Its equivalent formula can be :

$$\begin{gathered} L+R=2M \\ L+a=M \\ L+2a=R \end{gathered}$$

​ $L,R$ 是素数, $a$ 是$L,M,R$space,$M$ 是大于3的自然数.

​ From the formula we know every natural number$M$A pair of prime numbers appearing at the same distance on both sides is established,推广$L$Available numbers：

$$\begin{array}{cc}M& R\\ \frac{}{}& \frac{}{}\\ L_1+1& L_1+2\\ L_2+1& L_2+4\\ L_3+1& L_3+6\\ \dots & \dots \\ L_a+1& L_a+2a\end{array}$$

​ $L_a=\{2,3,...,a\},2a\in 2N,1\le a\le L_a$

$$M化为环\{\begin{array}{lrc}{P}_{1}N+a_1& & \\ P_{2}N+a_2& & 1<a_x<P_x\\ P_x+a_n& & \end{array}$$

$$R化为环\{\begin{array}{lrc}{P}_{1}N+a_1& & \\ P_{2}N+a_2& & 1<a_x<P_x\\ P_x+a_n& & \end{array}$$

​ $P_{x}N+a_n为整数循环$

​ 假设： 当且仅当 $\forall P_N+2a_n\notin P$ 时$\forall R\notin P$

​ To make current all$2a_n\in P_{x}N$back in the ring

​ 但是由于$\prod P_x+1\notin P$, 所以$\forall P_{x}N+2a_n\in P$ 不成立, 即$\exists R\in P$, It can be proved that the guess is established.

​ 例如：$M=7$时

$$\{\begin{array}{lrcccc}L& M=7& R& & & \\ 2& 2N+1& 2N+2& & & \\ 3& 3N+1& 3N+2& & & 存在L\in P同时R\in P,(L=3,R=11)\\ 5& 5N+2& 5N+4& & & \end{array}$$

​ ——Gechai is like an abyss,There may be gems in the dark,Mysterious and terrifying.