Goldbach Theorem ! r, g" I3 I7 i& I7 t' U$ I8 ]6 @0 W Union of set construction and analysis % M2 H& }7 y+ K9 {; d + ~3 Z0 m. d( N+ S( V$ N Loudi Xiaoguang mathematical research studio Su Xiaoguang . E: j8 E# i9 }& [6 R4 v6 [% Y 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) $ m; Z x0 v) {, ~! a5 uSo when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I " C6 [2 ]" \1 x- t) Y# vNot more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。 4 ?- A. j- O2 Y2 m1 pKey words: Germany,Goldbach,Union of set,even number, prime number, ( Y& a: E# w* ^ `# F" K/ c5 v
MR (2000) theme classification: 11 P32 " N) A; y1 X, A
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