Goldbach Theorem 1 T- m# p4 ^2 b9 V. ~$ e Union of set construction and analysis " Z9 X$ Z9 b- o+ D! y' T5 E% ~: R
Loudi Xiaoguang mathematical research studio Su Xiaoguang0 K' G1 s: `5 ?- M4 S" p
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)$ L- Y8 B Q7 f5 X, ?
So when N> 800000 when, D(N)No less than1.8432(1-1/logN)N/log^2_(N-2);I % ?; g6 r, c& O0 VNot more than5.0176[1+2/logN +o(1)]N/log[(N-2)/2]log(N-2)。, K% X7 i) C. F/ ?
Key words: Germany,Goldbach,Union of set,even number, prime number, ! N' p, {$ ~' N# j7 W9 B; p" K) DMR (2000) theme classification: 11 P32 % X, c1 L+ D9 ^$ P1 S
Email:suxiaoguong@foxmail. Com
Goldbach formula: % y4 F1 d3 u: E, n' b o 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]8 M$ }3 [/ P9 M5 Q3 C7 Q4 p; S
For N>800000,D(N) mean, P1 C( z* y) h _# i# a
N=P_1+P_2/ A0 A. {! N+ d* Y3 k
The number of elements。prime number P_1,P_2>2。 0 `! c7 I' E5 R' r: J 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 I; h" L; o( `7 P' { +[log N(N-2)/4]/[2 (log N/2)(log N/2)]# C$ k/ F) K, n
+{2 [log(N-2)/2] [log(N-2)/2]log N(N-2)}/[log N log N log(N-2)log(N-2)]