Goldbach Theorem / \6 Q. ?4 B3 k$ E2 ] Union of set construction and analysis9 z; I' ?0 c8 a2 E* p; @0 X
. }( [, L3 k2 r | Loudi Xiaoguang mathematical research studio Su Xiaoguang( n" L/ k U. X
Abstract: In the analytic number theory Goldbach problem is an important issue. The authors studied the:A={N │ N = (N-i) + i, N is a natural number, i belong to N} Clearly A is a countable set。C={N │ N = Pi + Pj, N is even number, Pi, Pj is prime number,i, j is natural number} Clearly, C is A subset。So C is a countable set.If x ={x|x no less than 6 and not more than N is an even number,x=P1+P2, P1, P2 is prime number},card (x)=M (x).Clearly, x is C subset。So x is a countable set.We can get the M(x) range,If N ={N|N = P1 + P2, N is even number, P1, P2 is prime number},card (N)=D(N),D(N)=M(N)-M(N-2) & }; [ T$ {4 u/ pSo when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I x! J. H3 m) `5 ~Not more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。5 j" Q/ j! _# F1 m, ]: B
Key words: Germany,Goldbach,Union of set,even number, prime number, : g5 C& ~9 D+ z" q) H/ u( B! y
MR (2000) theme classification: 11 P32 0 U! ?$ p e5 }' T/ lEmail:suxiaoguong@foxmail. Com