After the number "27" is substituted into the calculation method of the "hail conjecture", its rise and fall is very drastic.

Chen Zhou wrote a dense piece of scratch paper.

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

And this went through 77 steps of calculation.

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

It took another 34 steps of calculation.

In the hail conjecture, this calculation step is called hail distance.

And the entire hail journey of 27 takes a full 111 steps!

What's more, 9232 is already more than 27 times more than 342 times.

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

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

That's 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 class, Chen Zhou had some ideas about hail conjecture when he was looking for the direction of the topic.

The peculiarity of the number 27 is also 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 scratch paper.

Then take out a new piece of scratch 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 wasn't Chen Zhou's derivation, but what he saw.

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

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

But the number 4 is not included.

So, in the "hail tree", the number 16 is the first fork, followed by the number 64.

After that, every other number, a new tributary will be generated.

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

As Chen Zhou casually wrote down the conjecture of the hail he saw, Zhang Zhongyuan stood beside him at some point.

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

Then, Zhang Zhongyuan left Chen Zhou's side, wandered around at will, and returned to the podium.

Raising his hand on the whiteboard, he wrote the same number "27" as Chen Zhou.

"Bang Bang!" Zhang Zhongyuan clapped his hands and called some of his classmates back to their senses who were still playing this math game.

Then, he said, "Students, I walked around roughly and found that you have all the numbers. But when we make math games, we also need to find patterns, don't we?"

Under the podium, some students couldn't help but secretly think, didn't you say that you didn't talk about conjectures today, but only made games?

As if guessing what these students thought, Zhang Zhongyuan said: "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 glanced at Zhang Zhongyuan with interest.

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

Hearing Zhang Zhongyuan's words, many students who did not choose this number picked up the pen and listened to Zhang Zhongyuan's lecture while calculating.

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

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

This is a verification method based on the verification rules of the hail conjecture, and the purpose is to use an infinite sequence of numbers against 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 left and right, and the classmates around him were actually holding pens, not knowing what they were writing.

Are you still immersed in the amazing 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 by himself, Chen Zhou took the initiative to stand up and speak out for him: "Professor, this is a method to verify the hail conjecture by means of a number series according to the different tolerances of the number series. ”

"If the first term is an even number, and the tolerance is also an even number, then all the natural numbers on the sequence are even, and the whole series is divided by two. If the first term is odd, the tolerance is still even, then all the natural numbers on the sequence are odd, and according to the rules, you need to multiply the whole by 3 and add 1. ”

In the same way, if the first term is odd and the tolerance is also odd, then the odd terms must all be odd and multiply by 3 and add 1, and the even terms must be even, then divide by 2. If the first term is odd and the tolerance is even, then the odd terms must all be even, then divided by 2, and the even terms must all be odd, multiply by 3 and add 1. ”

"This is the sequence verification method. ”

As soon as Chen Zhou's words fell, he heard someone around him whispering: "The reason is such a reason, but there are more calculations and new problems in it." ”

Hearing this classmate's words, Chen Zhou didn't rush to sit down, so he continued: "But the number series verification method has many flaws. Because, according to such calculation rules, many new problems will be encountered. ”

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

After Chen Zhou finished speaking, he didn't continue to talk in depth.

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

With Chen Zhou's narration, the pens in the hands of many students have run faster, and they seem to be calculating along this line of thought.

After a while, they stopped writing.

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

Like everyone else, after putting down their pens, these people also turned their heads to look at Chen Zhou.

"Doesn't that mean it's a useless method?"

"I don't know, anyway, it's back to the original point. ”

"Hey, did you find out?"

"Found what?"

"The first person in the mathematics department is the first person, and I can see through the essence at a glance!"

"It's really awesome!"

"Actually, didn't you notice?"

"What did you find?"

"This question was told by Professor Zhang and was ready to be expanded, but it was finished by Chen Zhou, and then, I don't know how Professor Zhang is going to talk about it......"

These people's voices are not loud, or even deliberately low.

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

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