Prime numbers, that is, prime numbers.

It refers to a natural number greater than 1, which cannot be divided by other natural numbers except 1 and itself.

The number of prime numbers is infinite. Regarding this proof, the ancient Greek mathematician Euclid gave a classic proof as early as his book "The Origin of Geometry".

Also because the numbers of prime numbers are infinite, some people may ask, what is the distribution pattern of prime numbers?

How many prime numbers are there below 100,000?

How big is a random 100-digit number?

This has promoted the development of the pure mathematics subject of number theory, and has the Goldbach 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 infinite twin prime numbers, whether there are infinite prime numbers in the Fibonacci sequence, whether there are infinite Mason prime numbers, whether there are infinite prime numbers in the form x21, and so on.

Here, there are problems solved using the prime number theorem such as "between a number greater than 1 and twice its number, there must be at least one prime number" and "there is a prime arithmetic sequence of any length".

But more, it's just a guess.

If you want to classify, the Kramel conjecture that Chen Zhou is studying now is probably above the Mason prime number problem, and under the Jepov conjecture and the twin prime number conjecture.

So, Chen Zhou is a little confused now whether his thoughts are correct.

A mathematical conjecture that lasted nearly a hundred years and no one could get close to proofs, he actually found that it seemed something was wrong and needed to be corrected.

In fact, if you say something wrong, you will use the words inappropriately.

Because Chen Zhou did not falsify it, he just found the conjecture of the prime number spacing after "improved".

Just like the Love Toast conjecture proved by Tao Zhexuan and others in 2014.

What Chen Zhou improved was only a more gentle conjecture.

Even if proven, it does not mean that Kramel'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 that of Kramel's conjecture.

He put down his pen and reached out to rub his temples. Chen Zhou's expression was a bit strange.

On the draft paper, it says:

【Conjecture of the maximum interval between adjacent prime numbers within n, (pn1≤n)max(pn1-pn)≈logn(logn-loglogn)2(n≥7)】

Here n refers to any natural number greater than or equal to 7.

"log" is the abbreviation of natural logarithm.

The expression of Kramel's conjecture is [limn→∞sup(pn1-pn)/(logpn)2=1].

The difference between the two is to change (logpn)2 to logn(logn-loglogn)2, and n≥7.

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

Thinking of this, Chen Zhou picked up the pen again and planned to solve this improvement problem first.

Chen Zhou's solution is the same as the proof method of the Aitas conjecture, and is based on a simple method to establish large prime intervals.

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

Let’s give a brief example, start with the numbers 2, 3, 4,..., 101.

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

This column of numbers becomes 101!2,101!3,101!4,...,101!101.

Because 101! can be divided by numbers from 2 to 101, each number in this column is a composite number.

That is, 101!2 can be divisible by 2, 101!3 can be divisible by 3, and so on.

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

If it is possible to obtain a list of composite numbers, then we can use this to study the problem of prime number interval.

In the afternoon, Chen Zhou was studying the corrections of the Kramel conjecture in the library.

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

It was not like he tried to solve the Kramel conjecture in this way at the beginning.

At 6 pm, Chen Zhou and Yang Yiyi walked out of the library hand in hand.

Since we have returned to Yan University and the previous rhythm of study and life, Chen Zhou is naturally accompanied by Yang Yiyi.

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

Every time I put aside my pen, I can see my favorite girl when I turn my head. It's really great.

Originally, Yang Yiyi and she planned to go directly to the cafeteria to eat rice drizzle, but unexpectedly, Shen Jing called.

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

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

Chen Zhou replied: "Just come out of the library."

Shen Jing was silent for two seconds before saying, "Okay, you have no place to go except to the library..."

Chen Zhou said unhappily: "Who said that there is also the mathematical arts and the accelerator laboratory, I can go there!"

Shen Jing was silent. He wanted to say, is there anything besides learning and research?

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

Chen Zhouying said: "Okay, Yiyi and I will go to the cafeteria, come here."

When Chen Zhou and Yang Yiyi arrived at the canteen, Shen Jing was already waiting at the door of the canteen.

As soon as he saw Shen Jing, Chen Zhou asked with a smile: "Senior, how about it? Is it a good feeling left?"

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

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

Shen Jing glanced at Chen Zhou and said helplessly: "I thought it was like this, but the truth is not..."

Shen Jing immediately started to complain, interrupting him before he started to show off, and then he also helped Chen Zhou pretend to be slutty and vomited out all the reasons.

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

Yang Yiyi couldn't help but chuckled softly, "Senior, you are not sure of the opportunity. You just need to learn more about him, right?"

Hearing this, Shen Jing frowned and looked at the couple, and sighed softly: "Oh, I think 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 quipped: "A man, how can he say he can't do it?"

Shen Jing: “…”

Chen Zhou thought of Shen Jing saying on the phone that Dr. Wu had something to explain, so he asked, "Senior, did you say Dr. Wu explain something?"

Chen Jing nodded, pondered for a moment, and said, "I explained something. Dr. Wu hopes that you will not give up your talent in materials learning. She thinks you will definitely be able to achieve some achievements in this regard."

Chen Zhou waited for a while, and saw that Chen Jing seemed to have finished speaking, he asked, "It's gone? That's it?"

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

"No, nothing..." Chen Zhou was a little embarrassed. He thought Dr. Wu Xinyue had something to explain on the subject, but the result was this.

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

Chen Zhou: "Nothing...that's right, thanks to Dr. Wu for your concern, but, is that still necessary?"

Chen Jing: "..."

The few people chatted for a few more simple words, and Chen Zhou took out his cell phone and called.

Tonight, go out for a meal.

Now that Shen Jing is back, he just happened to call Fang Jieming up.

Fang Jieming agreed to help this topic without saying a word, but Chen Zhou still remembered it.
Chapter completed!