By Zhou M (2022).
|
Greener Journal of
Applied Mathematics and Statistics Vol. 2(1), pp. 10-11, 2022 Copyright ©2022, the
copyright of this article is retained by the author(s) http://gjournals.org/GJAMS |
|
An unsolved problem solution in number
theory
Suqian
Economy and Trade vocational School
|
ARTICLE INFO |
|
|
|||||||
|
Article
No.: 122821163 Type: Short Comm. |
Accepted: 10/12/2021 Published: 31/12/2021 |
*Corresponding
Author Zhou Mi E-mail: zhoumi19920626@ 163.com |
Keywords:
|
|
|||||
|
|
|
|
|
|
|
||||
There
is an unsolved problem in number theory：
q1=2,q2=3,q3=5,q4,q5…… Sequence of all prime numbers are arranged by size, then
Qk=q1*q2*q3…….qk+1
Q1=3,Q2=7,Q3=31,Q4=211,Q5=2311,Q6=59*509,Q7=19*97*277,Q8=347*27953,Q9=317*7037
63,Q10=331*571*34231 The first five numbers are prime number, The other five
numbers are composite number, it is not known whether there are infinitely k
let Qk is a prime number, it is also not known whether there are infinite lk
let Qk is a composite number. Now there is a solution: Look at a matrix: in
1934, one from the East Indies (now Bangladesh) ordinary scholar - Chandra, in
the field of number theory has made a brilliant achievement, this achievement
makes him leaving a legacy, immortal. Chandra square sieve the first row is the
square sieve is the first of 4, the difference between two adjacent numbers is
3 arithmetic sequence: 4,7,10, ... The second line, third line, ...... any
subsequent row are also arithmetic sequence, but the difference between two
adjacent numbers gradually become larger, respectively, 5,7,9,11,13, ... and
they are all odd . ...................................
4
7 10 13 16 19 22 25 ……
7
12 17 22 27 32 37 42 ……
10
17 24 31 38 45 52 59 ……
13
22 31 40 49 58 67 76
16 27 38 49 60 71 82 93 ……
19
32 45 58 71 84 97 110 …….
...................
his
square sieve secret is: If a natural number N appear in the table, then 2N +1
certainly not a prime number, if N does not appear in the table, then 2N +1 is
definitely a prime number. Let's look at a few examples. Beginning with 4,
skipped three numbers 1,2,3, of course, they will never appear in the table.
Then, 2 × 1 +1 = 3,2 × 2 +1 = 5, 2 × 3 +1 = 7. You see, 3,5,7 are prime
numbers. Look at the number 17, 17 is in the symmetric matrix ， 17*2+1=35
and 35 is a prime number. All primes can be launched from the table to the
inverse. Qk=q1*q2*q3，，，，*qk+1，q1=2,so
Q2=2*（q2*q3，，，，qk）+1,Obviously
q2*q3*q4，，，，*qk is a
composite number, so q2*q3*q4，，，，*qk=2N+1,if N is in
the matrix, Qk=2*(2N+1)+1，if 2N +1 appears in the matrix ,Qk is a composite number,
N appear in the matrix, There are infinite N in the matrix to make the 2N+1
appear in the matrix or not.so it has infinite Qk=2*(2N+1)+1 is a prime or not.
,So the conjecture has a possibility set up ! A new solution to solve the twin
prime conjecture Twin primes conjecture in number theory is a famous unsolved
problem . This conjecture can be described as "exist infinite number of
twin primes ." A difference of two twin primes pair of primes. For
example, 3 and 5 , 5 and 7, 11 and 13 , ... , 10016957 and 10016959 , and so
are twin primes . The method of my proof is as follows : Look at a matrix: in
1934, one from the East Indies (now Bangladesh) ordinary scholar - Chandra, in
the field of number theory has made a brilliant achievement, this achievement
makes him leaving a legacy, immortal. Chandra square sieve the first row is the
first of four, the difference between two adjacent numbers is 3 arithmetic
sequence: 4,7,10, ... (could have been written down, never write less head).
The second line, third line, ...... any subsequent row are also arithmetic
sequence, but the difference between two adjacent numbers gradually become
larger, respectively, 5,7,9,11,13, ... and they are all odd . 4 7 10 13 16 19
22 25 …… 7 12 17 22 27 32 37 42 …… 10 17 24 31 38 45 52 59 …… 13 22 31 40 49 58
67 76 16 27 38 49 60 71 82 93 …… 19 32 45 58 71 84 97 110 ……. This square sieve
secret is: If a natural number N appear in the table, then 2N +1 certainly not
a prime number, if N does not appear in the table, then 2N +1 is definitely
prime. Let's look at a few examples. Since the beginning of this table from the
four, skipped three numbers 1,2,3, of course, they will never appear in the
table. Then, 2 × 1 +1 = 3, 2 × 2 +1 =5, 2 × 3 +1 = 7. You see, 3,5,7 are prime
numbers. Look at the number in the table 17, which equals 1 plus 2 times 35 and
35 is not a prime number. Almost all primes can be launched from the table to
the inverse. In the first line of the matrix ，between the two
numbers are also two numbers and they do not appear in the matrix , such as 5
and 6,5 * 11,6 * 2 +1 = 2 +1 = 13,11 and 13 is a twin prime number, if without
the second row、 third row
and fourth row，，，
intervention，the
adjacent numbers do not appear in the first row which two times of them and
plus 1 are infinitely twin primes. In fact, even with their intervention, with
the number increases, the twin primes will become increasingly scarce, however
, the second line , third line , fourth line，，，，，can
impossible to completely cover the first row , so the twin primes is infinite.
|
Cite this Article: Zhou M (2022). |