Goldbach Theorem, q7 o' M1 K9 [7 C% ]7 S, h
Union of set construction and analysis 7 P; b; z c$ w0 m6 K$ C/ f( L" L9 v" k9 \/ j
Loudi Xiaoguang mathematical research studio Su Xiaoguang8 @6 O; _; y! l2 V" j3 J3 Z' s( U& [
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); E4 s6 B A$ q
So when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I " Y1 l! x9 Q5 x! A/ J+ U4 \# W: n- B4 w- iNot more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。 6 C1 Z( B7 G9 M2 U6 A% G# d$ RKey words: Germany,Goldbach,Union of set,even number, prime number, ! c* T) ]1 u) b- U# C* K" d2 }
MR (2000) theme classification: 11 P32 ' v2 G& [, m$ N# U( o% L6 @8 wEmail:suxiaoguong@foxmail. Com
Goldbach formula:" z9 Z) |! M) G
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] + x: D/ ?8 P0 U' u7 \" Q: m1 U7 i6 w. { AFor N>800000,D(N) mean 6 G9 p3 e1 b5 L) x- F N=P_1+P_24 U& A, d' s: i s1 q% b/ a$ E$ u2 `- a
The number of elements。prime number P_1,P_2>2。% g# N& y* W0 L+ C# T! w/ o
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]6 _% D \' N& a
+[log N(N-2)/4]/[2 (log N/2)(log N/2)] % ~, }# P2 K: C0 b +{2 [log(N-2)/2] [log(N-2)/2]log N(N-2)}/[log N log N log(N-2)log(N-2)]