Goldbach Theorem2 u1 J _$ ]) Z' F- l
Union of set construction and analysis- A3 v: }' R; h* ^/ X
9 z8 [% X3 X; H. d Loudi Xiaoguang mathematical research studio Su Xiaoguang n- R' W- K' w8 B 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)1 E e+ u/ V# i v* z
So when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I6 j+ k Z8 N3 C6 J
Not more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。 ! {8 T6 z: L# h9 F& a' ~! vKey words: Germany,Goldbach,Union of set,even number, prime number, * c' n2 K( T: v( N- t lMR (2000) theme classification: 11 P32 - f1 @8 P3 `: J3 d3 H
Email:suxiaoguong@foxmail. Com
Goldbach formula:+ n, G' b6 a8 H1 g/ N1 O& f' `
1.8432(1-1/log N)N/log(N-2)log(n-2)<D(N)<2.5088 S(N)N/[log(N-2)/2][log(N-2)/2]! Z5 |% g) z6 B( J+ G4 X: W
For N>800000,D(N) mean 2 ~( t4 S+ K E N=P_1+P_2 8 H1 h. C e3 rThe number of elements。prime number P_1,P_2>2。 4 }: Q" K3 \2 Z0 s S(N)=1-(2 log 2 log 2)/[log(N-2)log(N-2)]-2{[ log(N-2)/2]log N(N-2)}/[2 log N log(N-2)log N/2] : b8 H& T8 n' a4 |. L +[log N(N-2)/4]/[2 (log N/2)(log N/2)]7 a# @4 v7 S! @9 C2 r. m
+{2 [log(N-2)/2] [log(N-2)/2]log N(N-2)}/[log N log N log(N-2)log(N-2)]