Goldbach Theorem . ]3 P% K& z, Y9 C! F i5 Z Union of set construction and analysis; Y O8 T7 t( ` f: c( z
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Loudi Xiaoguang mathematical research studio Su Xiaoguang 1 r8 z, J: c2 m2 _) ]* a+ e1 R 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). f: r5 b5 ?6 W! t! T0 L7 d
So when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I 8 K% O3 b( ~' Y X6 ZNot more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。 + ]' P/ \! P0 K& B7 F1 yKey words: Germany,Goldbach,Union of set,even number, prime number, " q9 F* l! S- v% a8 h% d5 vMR (2000) theme classification: 11 P32 , A. u! y. b: o( _2 w4 @
Email:suxiaoguong@foxmail. Com