Xueba starts with change

Chapter 174 Give an Example
After the number "27" is substituted into the calculation method of "Hail Conjecture", its ups and downs are very violent.

Chen Zhou wrote a dense sheet of draft paper.

Because "27" didn't reach its peak until 9232.

And this has gone through 77 steps of calculation.

Subsequently, when "27" returned to the bottom value of 1.

After another 34 steps of calculation.

In the hail conjecture, this computational step is called the hail range.

And the full range of 27 needs a full 111 steps!
More importantly, 9232 is already 27 times more than 342.

If you compare it with a waterfall-like straight drop, that is, 2 to the Nth power.

The number with the same range is 2 to the 111th power.

What a huge number!

After such a comparison, we can see how the number 27 fluctuates violently.

The reason why Chen Zhou chose this number is also because of his understanding of the hail conjecture.

Before Zhang Zhongyuan's small class, Chen Zhou had some thoughts on the hail conjecture when he was looking for the direction of the subject.

The particularity of the number 27 lies in that it can only be changed from 54.

And 54 must have fallen from 108.

Chen Zhou stopped the pen in his hand and lightly tapped the draft paper.

Then take out a new draft paper and start writing [4k, 3m+1 (k, m is a natural number)].

This is something that has been verified by the rules of the game.

It's not what Chen Zhou came up with, but what he saw.

In the hail conjecture, only when there are numbers at both 4k and 3m+1, the fork of the "hail tree" can be generated.

The so-called bifurcation is the intersection with 2 to the Nth power.

But the number 4 is not included.

So, in the "Hail Tree", the number 16 is the first fork, and then the number 64.

Every other number in the future will produce a new tributary.

Therefore, above 27, there must be a powerful tributary.

While Chen Zhou was casually writing the conjectures about the hailstorm he saw, Zhang Zhongyuan stood beside him at some point.

Looking at what Chen Zhou wrote, Zhang Zhongyuan couldn't help raising his eyebrows, a little interesting.

Afterwards, Zhang Zhongyuan left Chen Zhou's side, wandered around casually, and then returned to the podium.

He raised his hand on the whiteboard and wrote down the same number "27" as Chen Zhou.

"Crack!" Zhang Zhongyuan clapped his hands, calling some students who were still playing this math game back to their senses.

Then, he said: "Students, I took a stroll around and found that you can substitute any number. But when we play math games, we also need to discover the rules, don't we?"

Under the podium, some students couldn't help thinking secretly, didn't you say that today you don't talk about conjectures, but just play games?

As if he had guessed the thoughts of these students, Zhang Zhongyuan said again: "Isn't it the fun of the game itself to discover the rules from the game?"

Glancing at the students under the podium, Zhang Zhongyuan deliberately stayed on Chen Zhou for two more seconds.

Chen Zhou looked at Zhang Zhongyuan with interest.

Looking back, Zhang Zhongyuan turned sideways and pointed to the number 27 on the whiteboard: "This is the most attractive number in this game, within the range of 1 to 100. Some students also chose it. I believe you have already experienced it." Come to its charm."

Hearing Zhang Zhongyuan's words, many students who did not choose this number picked up their pens and listened to Zhang Zhongyuan's lecture while counting.

After Zhang Zhongyuan said the number 27, he wrote down a few more words, and then asked, "Does any of you know the purpose of this method?"

Chen Zhou glanced at the words "number sequence verification method" on the whiteboard.

This is a verification method established according to the verification rules of the hail conjecture, and the purpose is to deal with infinite natural numbers with infinite series.

This can actually be understood literally.

But what Chen Zhou didn't expect was that no one took the initiative to answer this question.

Chen Zhou looked around, and the students around him were all holding pens, not knowing what they were writing.

Are you still immersed in the wonderful journey of 27?

Zhang Zhongyuan was also quite surprised. He finally looked at Chen Zhou again with a strange look in his eyes.

Chen Zhou naturally noticed this look.

Therefore, when Zhang Zhongyuan was about to answer the question by himself, Chen Zhou stood up on his own initiative and said it for him: "Professor, this is a method to verify the hailstone conjecture through the number sequence according to the different tolerances of the number sequence."

"If the first item is even and the tolerance is even, then all the natural numbers on the sequence are even, and the entire sequence is divided by 2. If the first item is odd and the tolerance is even, then all the natural numbers on the sequence are odd. According to the rules, You need to multiply the whole by 3 and add 1."

"Similarly, if the first item is odd and the tolerance is also odd, then the odd number must be odd, multiply by 3 and add 1, and the even number must be even, then divide by 2. If the first item is odd, the tolerance is an even number, then the odd-numbered items must be even numbers, then divide by 2, the even-numbered items must be all odd numbers, then multiply by 3 and add 1."

"This is the number sequence verification method."

After Chen Zhou's voice fell, he heard someone whispering around him: "The theory is such a theory, but there are more calculations and new problems in it."

Hearing what this classmate said, Chen Zhou didn't sit down in a hurry, so he continued, "But the number sequence verification method has many flaws. Because, if we continue to calculate according to such calculation rules, we will encounter many new problems."

After a pause, Chen Zhou smiled slightly: "For example, for the general term of even numbers, we usually express it as 2n, and n is a natural number. Because they are all even numbers, 2n needs to be divided by 2 to get n. This It goes back to the natural numbers, and it goes back to the problem itself.”

After Chen Zhou finished speaking, he didn't go any further.

At this point, we are already on the way to verify the hail conjecture.

And following Chen Zhou's narration, the pens in the hands of many students turned faster, as if they were following this line of thought and counting down.

After a while, they stopped writing.

Because, n is n, and it is still n after calculation...

Like the others, these people turned to look at Chen Zhou after putting down their pens.

"Isn't this a useless method?"

"I don't know, anyway, after calculations, I have returned to the original point."

"Hey, did you find out?"

"Found what?"

"No.1 in the Department of Mathematics is No.1, you can see through the essence at a glance!"

"It's really awesome!"

"Actually, didn't you find out?"

"What did you find again?"

"Professor Zhang raised this question and prepared to expand it, but it was finished by Chen Zhou. Next, I don't know what Professor Zhang is going to say..."

The voices of these people were not loud, and were even deliberately lowered.

But this is a small class after all, not like a big classroom.

Their words were still heard by Chen Zhou and Zhang Zhongyuan.

(End of this chapter)