Goldbach Theorem4 i" h4 ^0 n& [( ^; h+ @! @$ K
Union of set construction and analysis; F0 @% e5 h" x& [4 `- k
. l: E% u4 m8 E% w( }) Y+ \ Loudi Xiaoguang mathematical research studio Su Xiaoguang" r0 D1 {& v6 r3 C) j
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) ( A5 e! T3 a3 o1 I) |! |So when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I ! t2 }! P4 B9 c6 @6 { hNot more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。 6 n+ o) C4 c& t z/ f; m6 e9 TKey words: Germany,Goldbach,Union of set,even number, prime number, ' y1 u) k z! SMR (2000) theme classification: 11 P32 3 u: Y. r, Z2 S% T5 X; [' CEmail:suxiaoguong@foxmail. Com
Goldbach formula: : T- t# A" ?: u, ?+ f/ R 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] + {9 a E. \/ N5 _For N>800000,D(N) mean ( T( ]0 B+ L; c l1 M N=P_1+P_2# t# `* `% U' N' x9 ] z: C! P& M
The number of elements。prime number P_1,P_2>2。 0 L& u0 T9 Q2 x# d 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]. r' Q4 i* V- w$ f
+[log N(N-2)/4]/[2 (log N/2)(log N/2)]; ^' a4 q; N2 D
+{2 [log(N-2)/2] [log(N-2)/2]log N(N-2)}/[log N log N log(N-2)log(N-2)]