Goldbach’s Theorem

数学1+1

! ]% _& [) y  V
javascript:;

4 H7 I: _- R- `2 W
& w" V( [0 `3 m! a$ b

数学1+1

References
, f0 c0 U5 ?# n0 |[1]        G. H. Hardy , E. M. Wright, An Introduction to the Theory of Numbers, People's Posts and Telecommunications Press, Beijing,2009,1-13.
7 i$ e" ?; J2 Z1 Y: A[2]        Hua Luogeng，An Introduction to the Theory of Numbers, Science Press, Beijing,1979.85-112
[3]        Hua Luogeng，Hua Luogeng's anthology ｜ Number Theory Volume I｜ Science Press, Beijing,2010.199-217.
[4]        J. Barkley Rosser and Lowell Schoenfeld, Approximate formulas for some functions of prime numbers, Ill. Journ. Math. 6 (1962) 64-94.
9 l% b% C  I2 k5 _. U[5]        Knang Jichang, Applied inequalities, Shandong science and Technology Press,Ji'nan,2010.
346-358.
[6]        Pan Chengdong, Chinese Annals of Mathematics,Series B, 1982,3(4):555-560.
[7]        Pan Chengdong, pan Chengbiao，Analytical number theory basis，Harbin Institute of Technology Press，Harbin，2012,196-375.
: v5 I7 ?2 s( o/ g  F( H
/ O) n3 u- c/ Y; U* b( ]4 w# K

数学1+1

& g$ Z9 V- ]* ?: h( g# lAbstract  We Definition Collection of sums of prime numbers is a set all integers in,
the form of p+p’ (for Prime number p,p’ Not less than 3),which is recorded as M (x),According
( Q7 S% C5 b- s  l! D! y/ }7 i( x* F' Pto the prime number theorem with error termestimate the extreme value of M (x),
: D6 r9 E2 a) Q) K6 Xuse the Newton-Leibniz formula to calculate the value difference of M (x), and
5 G" `0 F: H* a! g" p  rderive Goldbach Theorem.
Key words  even numbers, Goldbach, Collection of sums of prime numbers , constant
MR(2010) Subject Classification  11P32
5 _" C5 @: F8 D! X' j7 L& V9 ]

* K$ k  ?3 g. l) v3 U" v6 }

数学1+1

, ~$ o/ k5 k& j3 L; N9 J3 @- n7 l

数学1+1

1 h; u7 M- T! _$ p" d. A 摘要:我们定义素数和的集合是所有整数的集合，p + p’（素数p，p’不小于3）的形式，记录为M（x），根据带有误差的素数定理估计M（x）的极值，使用Newton-Leibniz公式计算M（x）的值差，然后推导哥德巴赫定理。
  关键词:偶数，哥德巴赫，素数和集合，常数
# \+ h  W$ I: I. ~  MR（2010）主题分类11P32
8 \+ a! r% |5 A( \7 b* i6 b

1 E' f+ i6 C0 `# q2 Z% h* \( H
, I; y! B4 t6 C$ ^


# M8 q" b5 [. S! o( [' P+ U

+ L8 h) K' A1 j9 _: ]1 n8 {; l


# ?3 T. `5 P* \# J% V


0 f3 b, f1 ]/ k6 l

6 R: X1 H9 p) ?# ~4 R. U! W
. g" n2 l- x6 y
; _! m/ W8 V+ c5 D% Z! P


; z# x4 g8 L) w0 N8 S; D( u; T% r

/ F5 d" q6 e- W1 O/ C
6 L5 @, R6 V5 M







3 l8 m& G7 c7 Y+ p8 R
5 b6 H$ X/ w& j

3 f' b) L) M' w! |0 w  I
" b  r4 o9 G3 t2 {$ d5 w8 Y




. j( c9 B; k6 N* s2 g9 a0 F
  F$ y$ Q! h' L7 ~" A- Z





9 \. n. D( v: g3 h0 b

/ @2 V$ n8 a4 O4 O( n. a
# y3 q$ u& i+ d" O" G2 c5 t

9 J1 A" c* O2 |/ g) y! ?: X


3 N9 U! T3 _) ?' o. v' B

" Y$ _% w! G, k* L
$ [: T. C, L: O2 a% }2 z


/ Z9 z8 F4 C1 b# N
0 R/ t6 K2 P: n3 t1 Y' q. \
! Y# T' f! L; K- m9 Q

7 m3 N" h1 g: u3 d; ?; a




: f' M' J$ |2 L# |" o- Y
- \3 W0 K2 A. S0 G' h3 h
% y, b7 ?9 P* Y: F
  \( ^1 o6 c8 ?0 o9 x8 P5 k3 ]& h
  F2 }' _3 `( Y" [



$ V/ I5 u" a+ |0 ]# B




7 ^  U* n6 |4 Y! O

2 h- c$ @& Z% Q4 b0 J
$ N  M& x, E( B' c; ~. i

; h7 o4 o' L2 V
  F, b, a; q) ?/ @3 K, Y
- r0 u" w$ X% a' S, s
; U1 P- t6 F5 x
6 z7 [7 I' _9 I3 K; ]8 Z4 o, H
$ u3 D( s6 Z( Z



& z8 \, c! S# V


* z& Q: i0 ~7 N9 e* R' E


' U' ]  s0 `* `  U  X




/ S+ ^* ~. \; f/ S1 V

: A& t* b2 \* U! \, u( T

/ M( h# X, q! H7 P* z1 ^

) p& P! q: ?' ~
9 I9 ?4 }) H# F, N# U) J, w


- U8 o3 Q( v4 Q. y. R- P5 x
3 y3 z3 [/ J' ^& R  o3 Y

9 ?* N' @  O% m1 d7 u
, b3 v6 }, ~4 E( K3 }6 s* j  E* C
' V' O8 ^% t2 e: \

1 P7 w4 s6 d1 z- T






/ H& G/ r4 S1 n* P

: h5 j; [, ]; H

- |9 y* H5 v: t3 M, [6 I4 V: y& n
( R' r" M! l* Y# e0 |


  D2 f+ _6 e, B8 q" z
# }) o1 ?! \) ]) x: U' U( E

2 I  N0 w" P2 I7 {0 T


. E- b) p: |- k+ }: R

* a2 T/ `3 W+ b: [, I( h


) ?0 U7 U/ ^: l  o% V* m% b! e3 ^+ c- e


4 i$ F6 L7 q% Q, t! U- C1 S- g3 E

4 m6 v; A, t4 x% \& u9 T6 S

" c4 z' A% t/ y' W1 V
/ e/ P" f) {( y& t. g. T& _
3 o; Y8 M" r  K4 B) T6 Z+ _
% K- G7 q2 h3 ?9 k. q1 |3 k

* }/ e9 _, p2 |3 V% P

! Q0 {) R1 s9 F+ n* T* i& P
, [2 }# {% W. d
1 f# Z$ L+ j6 {8 @- r: L% E

6 X$ I( v4 a2 F* j; }; a" g

( v, l( I0 U% c



2 e$ q6 i, Z5 z  B, ~



7 `( F4 m! Q6 I  S. y2 T8 F0 b

+ N7 I+ q: U' a, v5 A$ J, Z. x- L/ H  P
# U% G6 I: i# L# x" s5 X; m
3 B/ `/ F% {& {; E, A
! \7 A" a! M6 q$ j* I7 X# B

0 }; Z1 b% B; J; e
0 x' [4 n7 ~, ?  x. ]: p; Y0 z

( ~; E' I" G: ~6 N$ V

8 t) Y* l/ _& m1 d" t! F, E

- ?: E; b+ k4 e8 t
; M7 m* s6 k8 ]$ `0 f




7 A7 P( E9 o1 W; J3 h( V# ?
* W& O9 z. V# Z' E: h
5 r0 ]" Q4 I- X  t1 a# ~- K
. y  q' w. R/ A. \1 n( p


7 m  H6 J& Q) i- G
  a1 V  o; q2 _' J7 j+ T
; S8 q# v5 _* b# }  H

  S6 c: H, O8 ^$ W4 Z
# l4 ]# t8 `: F% H" d
  [/ R4 T9 N3 T' _4 ~
9 N- b7 K2 L$ F1 x9 x$ {+ J
! m; `: q* f3 T- G4 y9 A


9 o; v# m& K; n) J/ p" c
& K0 h0 d" b3 e9 A% e
& d+ h$ z& z4 \) I3 ]1 K9 W  L9 P: X* Z2 S






# C& [, E$ }3 {( M" l2 M
3 r$ Z- M+ ~, ^8 v( p8 u+ ?( _



, C( w% {. i: K5 ]/ v$ ]9 V; D! x
) [5 y2 M8 ^5 R  B: r5 T" {6 v. U6 l


( Y: ?/ G) k+ d6 [
6 g5 g9 U0 O  r6 ~$ R
0 Z9 l+ L. ~3 y3 n( Q) J+ |
  |" P) l8 k  B  e2 k$ {' ~2 T

  w" x1 S0 g( A8 {1 G0 e0 D


0 N5 h5 W# F. f
, C" p/ Z- x' P7 y6 {- ~. P





& V" ^5 d% _& m$ e$ _! r: i9 [
0 ]! l& _* s$ S" G7 U



5 J8 q  @% t7 p' t1 A1 Q1 y

0 w5 Y' n# |" ^4 Q% b

9 u' m+ m) g3 n) y* ?9 O9 [$ r' C& D   



! l0 c7 a) H3 l" L& H  q; U: Q* u
$ ?4 |+ g" V2 e  \+ h

数学1+1

7 t! v4 e5 n) r- K; b0 R1 }


& M8 \' _  F, U1 o

数学1+1

I havesubmitted a new manuscript titled "Goldbach Theorem" forconsideration by Annals of Mathematics.

/ t3 [7 h4 y( N3 Y( `9 `
+ h! W4 @/ T, Y; M- s5 m, m8 s
  r7 v& ]( E1 H1 s( C1 m9 f' f