任何一个不小于6的偶数都可表为一对以上奇素数之和(英文版)

1、任何一个不小于6的偶数都可表为一对以上奇素数之和（英文版）Any Even Number no Smaller than 6 Can be the Sum of Over a Pair of Odd Prime NumbersMeng Qingyu（Email：mqyu36）Abstract:The purpose of this paper is to prove that “each even number no smaller than 6 can be the sum of two odd prime numbers” with the method of “graphic analy

2、sis, statistics and calculation” (1+1). (Note: prime numbers and composite numbers of this paper all refer to odd prime numbers and odd composite numbers)Key words: Prime numbers, distribution diagrams, figure A, figure B, template of the prime number, template of the composite number, prime numbers

3、, prime pairsI. Introduction N means any even number (), h is the serial number of N. Make the “prime number + prime number” of any even number interval , that is, (1+1) are all prime numbers. (1) (2) II. Introduction of new mathematical words and use of new calculation data1. Template of prime numb

4、ers definition: All composite numbers are excluded from the odd number sequence 3. The template of prime numbers and blank positions is the template of prime numbers which is represented by ph: 2. Template of the prime number definition: After counting the template of prime numbers, accumulate the t

5、emplate of the prime number and represent it with the symbol nh: 3. Template of composite numbers definition: All prime numbers are excluded from the odd number sequence 3. The template of composite numbers and blank positions is the template of composite numbers which is represented by Fh: 4. Templ

6、ate of the composite number definition: After counting the template of composite numbers, accumulate the template of the composite number and represent it with the symbol nh: In the above four templates figures, the first line is the template number, and the second line is the template. The template

7、 is corresponding to the number. For example, the 26th template of prime numbers, template of the prime number, template of composite numbers, and template of the composite number are 53, 15, blank, and 11 respectively. The unit of template is plate which constitutes the template. 5. “Difference of

8、prime numbers” definition: after the prime number subtracts 3 and divide 2, the value obtained will be the “difference of prime numbers” which is represented by pc. The formula is: pc=(Pn-3)/2;6. “Difference of composite numbers” definition: after the composite number subtracts 3 and divide 2, the v

9、alue obtained will be the “difference of composite numbers” which is represented by Fc. The formula is: Fc=(Fm-3)/2;III. Two distribution figures1. “(prime number + prime number) distribution figures” (figure A for short)Figure A is drawn by arranging even numbers and then subtracting prime numbers

10、through the template of prime numbers arrangement. 2. “(composite number + composite number) distribution figures” (figure B for short)Figure B is drawn by arranging even numbers and then subtracting composite numbers through the template of composite numbers arrangement.IV. Chart analysis 1. Figure

11、 A reflects the distribution law, number and x-y relationship (e.g. ) of “prime number + prime number” (represented by x, all numerical part within the triangle range on the lower right part of C8 in the figure) (the statistic is in the last two lines of the figure) and “composite number + prime num

12、ber” (represented by y, all blank part within the triangle range on the lower right part of C8 in the figure) objectively, comprehensively and directly. 2. Figure B reflects the distribution law, number and y-z relationship (e.g. ) of “composite number + prime number” (all numerical part within the

13、triangle range on the lower right part of F8 in the figure) (the statistic is in the last two lines of the figure) and “composite number + composite number” (represented by z, all blank part within the triangle range on the lower right part of F8 in the figure) objectively, comprehensively and direc

14、tly. 3. Through the study, observation and analysis on figure A and figure B, it is also found that the column length of each even number in figure A is the template of the prime number , so A is formed through the accumulation of , that is, . In addition, it can be obtained by using to subtract “th

15、e sum of prime difference”, that is, . The column length of each even number in figure B is the “template of the composite number” , so B is formed through the accumulation of , that is, . In addition, it can be obtained by using to subtract “the sum of composite difference”, that is, .4. Plus A wit

16、h B, we call it C, that is, . 5. Figure A and B are key basis for the formula verification. 6. Figure of the quantity relationship trend of the six sequencesV. Formula verification As can be known from figure A and figure B: So, A: xB:y Also (1) And (2) The formula can be verified. In the formula, i

17、s the total number of all (prime number + prime number) from the even number 6 to (e.g. “1+1”), h is the sequence number of even numbers , is the h-th template of the prime number, A is the value accumulated by the template of the prime number , B is the value accumulated by the template of the comp

18、osite number , is the odd prime number, .Despite of different calculation data used by the above two formulas, formula (1) uses two numbers for calculation (h and ), formula (2) uses three numbers for calculation (h, and the prime sum), the calculation results are the same. The above formula is an a

19、pproximate calculation equation, and the result may be with errors. According to the statistic of N=131072 (the actual value) and the calculated value (the approximate value), the relative error of even numbers from 6 to 16, 20, and 22 is 0, that of 18 is 5.6%, that after 24 is smaller than 4%, afte

20、r 48% is smaller than 3%, after 240 is smaller than 2%, after 2730 is smaller than 1%, after 42330 is smaller than 0.5%, after 91172 is smaller than 0.45%, and after 102062 is smaller than 0.44%. Seen from the trend of the above relative errors, with the increase of the even number, the relative err

21、or will gradually be reduced. After the even number 131072, the error will be smaller than 0.44% rather than larger than 0.44%. The parallel plot and overlap graph of the statistic and calculated value of x are attached: Use the consequent to subtract the antecedent , and their difference will divid

22、e 2 (round-off in case of indivisibility), which will be (1+1) prime pairs; if the difference after minus is an odd number, half of this even number will be a prime number, and there will certainly be a group of prime pair ().The parallel plot and overlap graph of the statistic and calculated value of the (1+1) “prime number” and “prime pairs” are attached:VI. Verifying (1+1) with the proof by contradictionAssume Make W=0 (assume “1+1” does not work) Then: Obviously, the left side is larger than the right side in the above formula That is: Therefore, W 0 , that is, for any given even number