Volume 1: Student Life Chapter 174: Give an Example

When the number "27" is substituted into the calculation method of the "hail hypothesis", its rise and fall are very dramatic.

Chen Zhou filled a whole piece of draft paper with dense writing.

Because "27" did not reach its peak until 9232.

This involved 77 steps of calculation.

Then, when "27" returns to the bottom value of 1.

Another 34 steps of calculation were performed.

In the hailstone conjecture, this calculation step is called a hailstone.

And the entire process of 27 requires exactly 111 steps!

More importantly, 9232 is more than 342 times of 27.

If we compare it to a straight line falling like a waterfall, that is 2 to the power of N.

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

What a huge number!

Through such a comparison, we can see how drastically the number 27 fluctuates.

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

Before Zhang Zhongyuan's small class, Chen Zhou had some ideas about the hail conjecture when he was looking for the direction of his research project.

The special thing about the number 27 is that it can only be derived from 54.

And 54 must have fallen from 108.

Chen Zhou put down his pen and tapped the draft paper lightly.

Then take out a new piece of draft paper and start writing [4k, 3m+1 (k, m are natural numbers)].

This is something that comes from the proven rules of the game.

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

In the hail conjecture, only numbers at 4k and 3m+1 can produce a fork of the "hail tree".

The so-called fork is the intersection with 2 to the power of N.

But the number 4 is not included.

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

After that, a new tributary will be generated every certain number of times.

Therefore, above 27, a powerful tributary will definitely appear.

When Chen Zhou was casually writing down the content of his conjecture about the hail he saw, Zhang Zhongyuan stood beside him without him knowing when.

Looking at what Chen Zhou wrote, Zhang Zhongyuan couldn't help but raise his eyebrows, it was quite interesting.

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

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

"Pa pa!" Zhang Zhongyuan clapped his hands, calling back the attention of some students who were still playing this math game.

Then he said, "Students, I took a quick look around and found that you can substitute any number. But when we play math games, we also need to find patterns, right?"

Under the podium, some students couldn't help but think secretly, didn't you say that we won't talk about guessing today and just play games?

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

After taking a look at the students below the podium, Zhang Zhongyuan deliberately stayed on Chen Zhou for two more seconds.

Chen Zhou looked at Zhang Zhongyuan with interest.

Retracting his gaze, Zhang Zhongyuan leaned sideways and raised his finger to point at the number 27 on the whiteboard: "This is the most attractive number in the range of 1 to 100 in this game. Some students have also chosen it. I believe you have already experienced its charm."

After hearing Zhang Zhongyuan's words, many students who did not choose this number picked up their pens and started calculating while listening to Zhang Zhongyuan's lecture.

After Zhang Zhongyuan said the number 27, he wrote down a few words and asked, "Does anyone know the use of this method?"

Chen Zhou glanced at the words "Series Verification Method" on the whiteboard.

This is a verification method established based on the verification rules of the hailstone conjecture. Its purpose is to use an infinite number series to deal with infinite natural numbers.

This can actually be understood just by looking at the literal meaning.

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

Chen Zhou looked around and saw that the students around him were all holding pens, but he didn't know what they were writing.

Are you all 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.

So, when Zhang Zhongyuan was about to answer the question himself, Chen Zhou took the initiative to stand up and said it for him: "Professor, this is a method to verify the hail conjecture through the method of number series based on the different tolerances of the number series."

"If the first term is an even number and the common difference is also an even number, then all the natural numbers in the sequence are even numbers and the entire sequence is divided by 2. If the first term is an odd number and the common difference is still an even number, then all the natural numbers in the sequence are odd numbers. According to the rule, we need to multiply all of them by 3 and then add 1."

"Similarly, if the first term is an odd number and the common difference is also an odd number, then the odd terms must all be odd numbers, so multiply by 3 and add 1, and the even terms must all be even numbers, so divide by 2. If the first term is an odd number and the common difference is an even number, then the odd terms must all be even numbers, so divide by 2, and the even terms must all be odd numbers, so multiply by 3 and add 1."

“This is the sequence verification method.”

As soon as Chen Zhou finished speaking, he heard someone whispering, "That's the logic, but the amount of calculations involved, as well as the new problems that arise, are much greater."

After hearing what the classmate said, Chen Zhou did not rush to sit down, so he continued: "But the series verification method has many flaws. Because, if we continue to calculate according to this calculation rule, we will encounter many new problems."

After a pause, Chen Zhou smiled and said, "For example, the general form of even numbers is usually expressed as 2n, where n is a natural number. Since they are all even numbers, 2n needs to be divided by 2, and we get n. This goes back to natural numbers, and also back to the problem itself."

After Chen Zhou finished speaking, he did not go into further details.

At this point, we are actually on the way to verifying the hail hypothesis.

As Chen Zhou continued to talk, many students' pens moved faster, as if they were following this line of thought and continuing to calculate.

Soon, they stopped writing.

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

Like everyone else, these people put down their pens and turned to look at Chen Zhou.

“Isn’t this a useless method?”

"I don't know. Anyway, after all the calculations, I'm back to the original starting point."

"Hey, did you find out?"

"What did you find?"

"The number one person in the mathematics department is the number one person. He saw through the essence at a glance!"

“It’s really awesome!”