Xueba starts with change

Chapter 271 Needless to say?

Prime numbers, that is, prime numbers.

Refers to a natural number greater than 1 that cannot be divisible by other natural numbers except 1 and itself.

The number of prime numbers is infinite. As for the proof of this point, the ancient Greek mathematician Euclid gave a classic proof in his book "Elements of Geometry".

Also because the number of prime numbers is infinite, some people may ask, what is the distribution law of prime numbers?
How many prime numbers are there below 100000?

How likely is a random 100-digit number to be prime?
This also promotes the development of the pure mathematics subject of number theory, and there is Goldbach's conjecture whether every even number greater than 5 can be written as the sum of two prime numbers.

There are also questions such as whether there are infinitely many twin prime numbers, whether there are infinitely many prime numbers in the Fibonacci sequence, whether there are infinitely many Mersenne prime numbers, whether there are infinitely many prime numbers in the form of X+1, and so on.

Among them, there are problems solved by using the prime number theorem, such as "between a number greater than 1 and its 2 times, there must be at least one prime number", "there is an arithmetic sequence of prime numbers of any length".

But more is just a guess.

If you want to classify, the Krammel conjecture that Chen Zhou is currently studying is probably above the Mersenne prime number problem, and below the Jebov conjecture and the twin prime number conjecture.

Therefore, the current Chen Zhou is not sure whether his thinking is right or not.

A mathematical conjecture that has lasted for nearly a hundred years and no one has been able to come close to proving, he actually found something wrong and needed to be corrected.

In fact, if you say something wrong, the words you use are inappropriate.

Because Chen Zhou didn't falsify it, but just found the conjecture of the "improved" prime number spacing.

Just like in 2014, Terence Tao and his colleagues proved the Erdous conjecture.

What Chen Zhou improved was only a milder conjecture.

Even if it is proved, it does not mean that Kramer's conjecture is wrong.

And its value is less than Caramel's conjecture.

Because of the improved problem, the prime interval is still smaller than Krammel's conjecture.

Putting down the pen, he stretched out his hand to rub his temples, Chen Zhou had a weird expression.

On the draft paper, it was written:

[Conjecture on the maximum interval between adjacent prime numbers within N, (Pn+1≤N)max(Pn+1-Pn)≈logN(logN-loglogN)+2(N≥7)】

N here refers to any natural number greater than or equal to 7.

"log" is short for natural logarithm.

The expression of Krammel's conjecture is [limn→∞sup(Pn+1-Pn)/(logPn)=1].

The difference between the two is that (logPn) is changed to logN(logN-loglogN)+2, and N≥7.

If we can get a little inspiration from the solution of this problem, we may be able to solve the problem of Kramer's conjecture.

Thinking like this, Chen Zhou picked up his pen again, planning to solve this improvement problem first.

The idea of ​​Chen Zhou's solution is the same as the proof method of the Erdous conjecture, which is based on a simple method of establishing a large prime number interval.

A large prime interval is equivalent to a long list of non-prime numbers, or composite numbers, between two prime numbers.

To give a simple example, start with the numbers 2, 3, 4, ..., 101.

Then add the factorial of 101 to each number, which is 101! .

这列数字就变成了101！+2，101！+3，101！+4，……，101！+101。

Because 101!Divisible by numbers from 2 to 101, so each number in the list is a composite number.

也就是101！+2可以被2整除，101！+3可以被3整除，以此类推。

This simple method is actually a slight deformation of the high school algebra method.

If it were possible to obtain a list of composite numbers, then it would be possible to study the problem of intervals between prime numbers.

In the afternoon, Chen Zhou was in the library, devoting himself to the revision of Kramer's conjecture.

Although the problem was not solved, the research methods of Tao Zhexuan and other five professors still gave Chen Zhou a lot of gains.

It's not like he tried to use this method to solve Krammel's conjecture at the beginning.

At six o'clock in the afternoon, Chen Zhou and Yang Yiyi walked out of the library hand in hand.

Now that he has returned to Yan University and returned to the previous pace of study and life, Chen Zhou is naturally accompanied by Yang Yiyi.

This state is also the state Chen Zhou is most familiar with and likes.

Every time I put down the pen, I can see the girl I love the most when I turn my head, which is really good.

Originally, Yang Yiyi and Yang Yiyi planned to go directly to the cafeteria to eat rice bowls, but they didn't expect Shen Jing to call.

Chen Zhou answered the phone: "Senior, are you back?"

Shen Jing said: "Yes, just arrived at school, where are you?"

Chen Zhou replied, "I just came out of the library."

Shen Jing was silent for two seconds, and then said: "Well, you have nowhere to go except to the library..."

Chen Zhou was immediately unhappy and said, "Whoever said that, there is also the Institute of Physics and the Accelerator Laboratory, I can go there!"

Shen Jing remained silent, he really wanted to say, besides study and research, are there any other places?

But Shen Jing didn't say that in the end, he said: "I'll come to you, Dr. Wu has something to say."

Chen Zhou replied: "Okay, Yiyi and I are going to the cafeteria, come here."

When Chen Zhou and Yang Yiyi came to the canteen, Shen Jing was already waiting at the entrance of the canteen.

As soon as he saw Shen Jing, Chen Zhou smiled and asked, "Senior, how are you doing? It feels good to stay here, right?"

Hearing this, Shen Jing said angrily, "I'm not happy!"

Chen Zhou asked in surprise: "How is it possible? I have already left, they must have many questions chasing after you? Isn't this your performance time?"

Shen Jing glanced at Chen Zhou, and said helplessly, "I thought that was the case too, but the truth is not..."

Shen Jing immediately started complaining, before he started pretending to be aggressive, he was abruptly interrupted, and then he helped Chen Zhou pretend to be aggressive, and vomited it all out.

After hearing this, Chen Zhou couldn't help laughing out loud.

Yang Yiyi couldn't help laughing softly from the side: "Senior, it's because you didn't seize the opportunity, you can learn more from him, isn't it all right?"

Shen Jing heard the words, frowned and looked at the couple, and sighed lightly: "Oh, I thought so too, but I can't learn it! He can learn so many things in a week and solve the problem, but I can't... ..."

Chen Zhou held back his smile and jokingly said, "Man, how can you say you can't do it?"

Shen Jing: "..."

Chen Zhou remembered that Shen Jing said on the phone that Dr. Wu had something to say, so he asked, "Senior, you said that Dr. Wu has something to say?"

Shen Jing nodded, pondered for a while, and said, "I have explained something. Dr. Wu hopes that you will not give up your talent in material science. She thinks you will be able to make some achievements in this area."

Chen Zhou waited for a while, and seeing that Shen Jing seemed to have finished speaking, he asked, "No more? That's it?"

Shen Jing looked at Chen Zhou in confusion: "That's all, what's wrong?"

"No, it's nothing..." Chen Zhou was a little embarrassed. He thought that Dr. Wu Xinyue had something to explain, but it turned out to be this matter.

Shen Jing: "What do you think it is?"

Chen Zhou: "It's nothing... Well, thank you Dr. Wu for your concern, but, does it need to be said?"

Shen Jing: "..."

After a few people chatted briefly, Chen Zhou took out his mobile phone and made a call.

In the evening, let's go out for a meal.

Now that Shen Jing came back, he happened to call Fang Jieming.

Fang Jieming agreed to help with this project without a second thought, and Chen Zhou still remembered it.

After reconciling with Fang Jieming, the four of them went straight out of the school gate and found a grilled fish shop nearby.

(End of this chapter)