By Zhou M (2022).

 

Greener Journal of Applied Mathematics and Statistics

Vol. 2(1), pp. 12-14, 2022

Copyright ©2022, the copyright of this article is retained by the author(s)

http://gjournals.org/GJAMS

 

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The law of twin prime numbers

 

 

Mi Zhou

 

 

Suqian Economy and Trade vocational School

 

 

 

ARTICLE INFO

 

 

Article No.: 122821164

Type: Short Comm.

 

Accepted:  10/12/2021

Published: 31/12/2021

*Corresponding Author

Zhou Mi

E-mail: zhoumi19920626@ 163.com

 

Keywords: Chandra matrix, number theory, conjecture.

 

 

 

 

 

 

 

 

 

 

 

New digital Black holes and hail conjecture

 

"In mathematics, there is a phenomenon called 'digital black hole', black hole number is also called trap number, a kind of integer with peculiar transformation characteristics, any number by finite rearrangement difference operation, always get some number.

 

The Sisyphus black hole, or 123 number black hole,

 

Set an arbitrary string of numbers and count the number of even numbers, odd numbers, and the total number of digits contained in the number

For example: 1234567890,

Even: count the number of even digits in the number, in this case 2,4,6,8,0, making a total of five.

Odd: count the odd number of digits in the number, in this case 1,3,5,7,9, there are five in total.

Total: Count the total number of digits in this number, 10 in this example.

New number: put the answer in the order of "even-odd-total" and get the new number: 5510.

Repeat: the new number 5510 is repeated according to the above algorithm, and the new number 134 can be obtained.

 

Repeat: the new number 134 is repeated according to the above algorithm to obtain the new number 123.

Conclusion: logarithm 1234567890, according to the above algorithm, the final result must be 123, we can write a computer program, test for any number of a finite number of repetitions will be 123. In other words, the end result of any number cannot escape 123 black hole.

Caprekar black hole

 

Three-digit black hole 495:

 

As long as you enter a three-digit number, require that the digits be different from each other, such as 111,222, etc. So you take the three digits of this three-digit number and rearrange them in order of size to get the largest and smallest number, subtract them to get a new number, rearrange them in the same way, subtract them again, and you always get 495.

 

For example: enter 352, the largest digit 532, the smallest digit 235, subtract 297; If you rearrange it, you get 972 and 279, subtract 693; Then you get 963 and 369, and you subtract 594; So you get 954 and 459, and you subtract 495.

Four-digit black hole 6174:

 

Take the four digits of a four-digit number from the smallest to the largest to form a new number, and from the smallest to the smallest to form a new number, subtract the two numbers, and then repeat the process, as long as the four digits of the four-digit number do not repeat, the number will eventually become 6174.

For example, 3109, 9310-0139 = 9171, 9711-1179 = 8532, 8532-2358 = 6174. And 6174 is going to be 6174, 7641 minus 1467 is 6174.

 

Any four-digit number, as long as the four digits are not identical, is arranged in descending order, forming the largest number as the minuend; If the smallest number is subtracted in ascending order, the difference will be 6174. If it is not 6174, then subtracting by the above method, at most 7 steps, will inevitably get 6174.

For a four-digit number 5679, perform the following operations:

 

9765-5679 = = 4086864 0-0486 = 8172,

8721-1278 = 7443, 7443-3447 = 3996,

9963-3699 = 6264, 6642-2466 = 4176

7641-1467 = 6174

There are many more.

 

New digital black holes:

 

Write a string of numbers, first the number of prime numbers, then the number of composite numbers, and finally the number of prime numbers and the sum of composite numbers, will fall into the black hole of 202. For example, 1234567 becomes 426 the first time, 123 the second time, 202 the third time, and 202 no matter how many times. For example, 123456789, 448 the first time, 033 the second time, 202 the third time, right? Fell into the black hole of 202."

 

One day in 1976, the Washington Post ran a math story on its front page. The story goes like this:

In the mid-1970s, there was a simple game: Write an arbitrary natural number N and transform it as follows:

If it's an odd number, then the next step becomes 3N plus 1.

If it's an even number, then the next step becomes N/2.

Not only students, but also teachers, researchers, professors and academics have joined in. Why the game's enduring appeal? Because it turns out that no matter what number N is, you can't escape back to bottom 1. To be precise, there is no escape from the 4-2-1 cycle at the bottom.

This is known as the "hail Conjecture". The phenomenon is called the hail conjecture because it evaporates and crystallizes like a hailstone.

Any lift to continue to say: "let's look at a few examples, 12-6-3-10-5-16-8-4-2-1-4-2-1... I fell into a cycle of 4, 2, 1."

 

The new Hail conjecture:

 

Write a number N, if N is even you multiply it by 2 plus 1, if N is odd you multiply it by 1 and divide it by 2, and you do that again and again and you end up in a 5, 3, 2 cycle. For example, if N=13, the operation is 13-7-4-9-5-3-2-5-3-2......

 

 

 

Cite this Article: Zhou M (2022). The law of twin prime numbers. Greener Journal of Applied Mathematics and Statistics, 2(1): 12-14.