ログイン加法的整数論
2014/01/06
Additive number theory
「all even numbers of 6 or more is represented by the sum of two primes.
I divided integer into groups of six
6x 6x＋1 6x＋2 6x＋3 6x＋4 6x＋5
（x is Positive integer）
Of this 6x 6x＋2 6x＋4 are Even
6x+3 is Multiple of three
Only 6x+1 6x+5 prime exist（２，３ are expected）
Even is 6x or 6x+2 or 6x+4
I think about 6ｘ＋4
When we expressed in the sum of two odd
These begin （6x－1）+ （6x－1）
Further I divided 6x－1 into groups of five
①30x+5 ②30x+11 ③30x+17 ④30x+23 ⑤30x+29
About these 30x＋22
①＋① ②＋⑤ ③＋④ are 30x+10
②＋② ①＋③ ④＋⑤ are 30x＋22
③＋③ ①＋⑤ ②＋④ are 30x+4
④＋④ ①＋② ③＋⑤ are 30x+16
⑤＋⑤ ①＋④ ②＋③ are 30x+28
For example thinking about ④＋⑤
we think ④and⑤ are Arithmetic progression
☆ 1 2 3 4 5 6 7 ・・・
④ 23 53 83 113 143 173 203 ・・・
⑤ 29 59 89 119 149 179 209 ・・・
In this Arithmetic progression , there are only Multiple of prime numbers greater than or equal to 7 or Prime
（For numbers,I think them as a multiple of smallest prime factors,）
Further for example
about１４２（☆＝４）the combinations of ④＋⑤ are four kinds （The number is a）
As it is 13 ^ 2 or less and ☆＝４,
combinations comprising numbers not prime of the combinations are one kind
（The number is b）
Thinking about a-b when ☆＝５
When☆４→５, It is greater than 11 ^ 2、and it becomes Multiple of 11 can exist
There one by one is a multiple of 11 and a multiple of 7（119、143）（7･7･7、11･13）
Therefore a-b=3
If ④＋⑤changes other,※
At most there are two multiple of 7 and one Multiple of 11 Multiple of primer is two or less
a-b is two or more
Paradox
☆ Increases and think of a-b=0
however、as it is Square value, There is no possibility that Increased amount of☆,while it becomes next multiple of primer can exist is decreased.
In other words, There is no possibility that amount of a is decreased.
May exist prime number becomes exist newly is decreased.（1/7→1/11→1/13→1/17・・・）
In other words, There is no possibility that amount of a is increased.
, There is no possibility that a-b=0
And ④＋⑤changes to other ※ex①＋① ②＋⑤ ③＋④ ④＋④ ①＋② ③＋⑤
②＋② ①＋③ ③＋③ ①＋⑤ ②＋④ ⑤＋⑤ ①＋④ ②＋③、
And about all even numbers of 142 or less,infact it consists.
So This expectation correct about the even numbers 6x-4.
In the same way, we can say this expectation correct about the even numbers 6x and 6x+2.
「all even numbers of 6 or more is represented by the sum of two primes.
I divided integer into groups of six
6x 6x＋1 6x＋2 6x＋3 6x＋4 6x＋5
（x is Positive integer）
Of this 6x 6x＋2 6x＋4 are Even
6x+3 is Multiple of three
Only 6x+1 6x+5 prime exist（２，３ are expected）
Even is 6x or 6x+2 or 6x+4
I think about 6ｘ＋4
When we expressed in the sum of two odd
These begin （6x－1）+ （6x－1）
Further I divided 6x－1 into groups of five
①30x+5 ②30x+11 ③30x+17 ④30x+23 ⑤30x+29
About these 30x＋22
①＋① ②＋⑤ ③＋④ are 30x+10
②＋② ①＋③ ④＋⑤ are 30x＋22
③＋③ ①＋⑤ ②＋④ are 30x+4
④＋④ ①＋② ③＋⑤ are 30x+16
⑤＋⑤ ①＋④ ②＋③ are 30x+28
For example thinking about ④＋⑤
we think ④and⑤ are Arithmetic progression
☆ 1 2 3 4 5 6 7 ・・・
④ 23 53 83 113 143 173 203 ・・・
⑤ 29 59 89 119 149 179 209 ・・・
In this Arithmetic progression , there are only Multiple of prime numbers greater than or equal to 7 or Prime
（For numbers,I think them as a multiple of smallest prime factors,）
Further for example
about１４２（☆＝４）the combinations of ④＋⑤ are four kinds （The number is a）
As it is 13 ^ 2 or less and ☆＝４,
combinations comprising numbers not prime of the combinations are one kind
（The number is b）
Thinking about a-b when ☆＝５
When☆４→５, It is greater than 11 ^ 2、and it becomes Multiple of 11 can exist
There one by one is a multiple of 11 and a multiple of 7（119、143）（7･7･7、11･13）
Therefore a-b=3
If ④＋⑤changes other,※
At most there are two multiple of 7 and one Multiple of 11 Multiple of primer is two or less
a-b is two or more
Paradox
☆ Increases and think of a-b=0
however、as it is Square value, There is no possibility that Increased amount of☆,while it becomes next multiple of primer can exist is decreased.
In other words, There is no possibility that amount of a is decreased.
May exist prime number becomes exist newly is decreased.（1/7→1/11→1/13→1/17・・・）
In other words, There is no possibility that amount of a is increased.
, There is no possibility that a-b=0
And ④＋⑤changes to other ※ex①＋① ②＋⑤ ③＋④ ④＋④ ①＋② ③＋⑤
②＋② ①＋③ ③＋③ ①＋⑤ ②＋④ ⑤＋⑤ ①＋④ ②＋③、
And about all even numbers of 142 or less,infact it consists.
So This expectation correct about the even numbers 6x-4.
In the same way, we can say this expectation correct about the even numbers 6x and 6x+2.
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