Goldbach Theorem8 X1 V7 F F2 }5 E0 M4 f+ O
Union of set construction and analysis ! j) G0 ~6 a7 p& k+ W+ k4 F . h. o& T. S6 @( n9 ?9 M Loudi Xiaoguang mathematical research studio Su Xiaoguang6 @8 m. c' z; {) 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)/ x f& x1 p+ T7 F s5 R' o* g
So when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I$ Y! n c, X7 x: P X C! m1 k
Not more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。/ w7 [# E' W/ q' b7 g. \! Z
Key words: Germany,Goldbach,Union of set,even number, prime number, + ]. U" g0 k! R3 T# m0 ~; D, ~
MR (2000) theme classification: 11 P32 ( E s! m, F6 H+ w [* PEmail:suxiaoguong@foxmail. Com