Goldbach's conjecture and its extension - KYT's conjecture - prime numbers pattern
Hello, I am Bob, a junior high school student from Taiwan. I did some research on the disassembly of prime numbers for months and Made my own assumptions - KYT's conjecture. I don't expect to prove Goldbach Conjecture is wrong. But I seem to have found a prime numbers pattern between the two even numbers (in the same number group). Here is what I found the pattern and it is my blog, Please have a look at it.
The author of this article is Bob KYT. The following article was translated by Google and modified by Gary. Some expressions may not be smooth because of the language. But still thanks to google translate :-)
The author of this article is Bob KYT. The following article was translated by Google and modified by Gary. Some expressions may not be smooth because of the language. But still thanks to google translate :-)
Goldbach's conjecture and its extension -
KYT's conjecture
1. Accidental discovery - When the even
number is used for the following group analysis (the adjacent group of the same
group has a difference of 18) -
20 = 2+0=2 ← 2 is a single digit stop (2 is a group)
114 = 1+1+4= 6 ← 6 is a single digit that stops (6 is a group)
148 = 1+4+8=13 ←13 is not a single digit, then continue to add 1+3=4 ← 4 is a single digit that stops (4 is a group)
After trying to demolish 50 numbers, I
found that there is an interesting phenomenon, and the numbers will appear in
the cycle of 2, 4, 6, 8, 1, 3, 5, 7, and 9 (The numbers can be divided into 9
groups), so I divide the even numbers less than 1000 into 9 groups one by one,
even numbers >=8, all Found that there are the same rules, when the same
group of numbers is split into two prime numbers, the same prime number
appears, Another larger even number must also be a prime number (the difference
of 18).
For example
8=3+5
8=3+5
26=3+23 or 7+19 or 13+13
44=3+41 or 7+37 or 13+31
2. Because want to know if the same
phenomenon can be observed continuously in larger numbers, try disassembling
10000, 10018, 10036
The partial combination of these three
numbers, After observation, I found the same result, even numbers separated by 18, when the same
prime number appears after disassembly, plus Another prime number will be found
on multiples of 18 and 18. The discovery is also true -
For example
10000= 4517+5483
10000= 4517+5483
10018= 4517+5501
10036= 4517+5519
Therefore, it also triggered my hypothesis
(KYT conjecture, KYT's conjecture):
1. Even number >=8, according to the
above-mentioned number grouping method, the prime numbers separated by the
adjacent even numbers between the same group must have a common prime number,
and the two prime numbers separated by the adjacent even numbers are deducted.
The common prime number, the other larger even factor must also be a prime
number (a difference of 18).
2. This method can help to find the prime
number and factorization.
Unsolved questions:
More explanation about KYT's conjecture is described as follows:
a is a positive integer and is even,
a>=8, b=a+18, a=c+D, c, D,E are prime numbers.
a=c+D
b=c+E
E=D+18=b-c
There must be a prime number c that satisfies the two equations above.
More examples are as follows:
10=3+7;5+5
28=5+23;11+17
46=3+43;5+41;17+29;23+23
64=3+61;5+59;11+53 ;17+47;23+41
82=3+79;11+71 ;23+59;29+53;41+41
.......
.......
10000= 4517+5483
10018= 4517+5501
10036= 4517+5519
Unsolved questions:
When you split a group's adjacent numbers,
another prime number is found when a multiple of 18 or 18 is added to the same
prime number. Is this rule continuous in large prime numbers and still valid?
If it is established, is it helpful to find the next larger prime number? Can
it also be one of the ways to find a prime number?
If you need more detailed information,
please contact me here, I will explain as much as possible, this article is
also open reference, but the referrer must state the source of this blog. …KYT.
Start further research...
Start further research...
KYT's conjecture seems could be rewritten as below. - this one is better.
a is a positive integer and is even, a>=8, b=a+6, c, D,E are prime numbers.
a=c+D
b=c+E
E=D+6=b-c
There must be a prime number c that satisfies the two equations above.
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