Goldbach's conjecture originally stated that any integer greater than 2 could be written as the sum of three prime numbers.

Later, because of the cash math prize, the convention of "1 is also a prime number" was no longer used.

The statement of the original conjecture becomes that any integer greater than 5 can be written as the sum of three prime numbers.

As for the conjecture that is common today, it is the equivalent version proposed by Euler in his reply to Goldbach.

That is, any even number greater than 2 can be written as the sum of two prime numbers.

The equivalent conversion here is very simple.

Start with n>5.

When n is even, n=2+(n-2), n-2 is also even, which can be decomposed into the sum of two prime numbers.

When n is an odd number, n=3+(n-3), n-3 is also an even number and can be decomposed into the sum of two prime numbers.

This is also known as the "strong Goldbach conjecture", or the "Goldbach conjecture about even numbers".

While thinking, Chen Zhou wrote down some necessary content on scratch paper.

For the study of mathematical conjectures, the formulation of conjectures, the formulation of conjectures.

This is the first and most important step.

Habitually took a pen and clicked on the scratch paper, Chen Zhou left a section empty in the middle of the scratch paper, and then drew a horizontal line.

Below the horizontal line, Chen Zhou wrote the words "weak Goldbach conjecture".

Then, Chen Zhou continued to write something on the scratch paper about the weak Goldbach conjecture.

The so-called "weak Goldbach conjecture" is deduced from the "strong Goldbach conjecture".

It states that "any odd number greater than 7 can be written as the sum of three prime numbers".

As for the "distinction between the strong and the weak", if the "strong Goldbach conjecture" is true, then the "weak Goldbach conjecture" must be true.

Relatively, the difficulty of the two is not the same.

In 2012 and 2013, Peruvian mathematician Harold Hoovgot published two papers in which he announced that the weak Goldbach conjecture had been completely proved.

Later, Herovgolt's colleagues also used a computer to verify the proof process.

Therefore, the weak Goldbach conjecture derived from the strong Goldbach conjecture was finally solved first.

The latest research results of Qianggoldbach's conjecture are still based on the detailed proof of "1+2" published by Mr. Chen in 1973.

After that, there was little progress on the Jongoldbach conjecture.

Although in 2002, someone made something.

However, it is difficult to say that there has been substantial progress.

As for the weak Goldbach conjecture proved, the corresponding results have not been applied to the strong Goldbach conjecture by translation.

Regarding this point, Chen Zhou remembered that Tao Zhexuan seemed to have said it.

One of the basic techniques for studying the weak Goldbach conjecture is the method of Hardy-Littlewood and Vinogradov.

It is unlikely that it can be used in the Jan Goldbach conjecture.

The study of Giangoldbach's conjecture is basically limited to the category of analytic number theory.

Chen Zhou has also studied the methods of proving weak Goldbach's conjecture, including the basic technique.

He still quite agrees with Tao Zhexuan's point of view.

This is also the reason why the Jongoldbach conjecture is difficult.

On the one hand, people don't seem to be able to find any new tools.

On the other hand, at the moment, it seems that the connection with other fields of mathematics is very weak.

It's hard to do that.

In contrast, for the Riemann conjecture, almost every few years, some new discoveries are made.

Moreover, some of these discoveries are based on operator theory, some are based on noncommutative geometry, and some are based on analytic number theory.

And, from time to time, some mathematicians will excitedly announce that they have proved the Riemann hypothesis.

In this way, in fact, it creates a dilemma for the study of Goldbach's conjecture.

That is, there are really not many mathematicians who are really committed to doing it.

Mathematical research, including physical research, is actually a meal of youth.

Most of the mathematical and physical achievements were proposed when the researcher was young.

Therefore, for such a difficult mathematical conjecture as Gochai.

Most mathematicians are unwilling to take this lonely, youth-consuming path of Shura.

Speaking of which, there is another very embarrassing reason.

The number of people who study Gochai, after a gradual decrease.

Go out to an academic conference and you'll find that there's no one to discuss ideas with you.

Of course, Chen Zhou dared to take such a lonely path of Shura.

For him, isn't the previous Clamel conjecture also known as "no one can come close to proof"?

But in the end, didn't he turn it into Cramel's theorem?

Wasn't Jepov's conjecture, one of the two most important conjectures in the prime interval problem, also proved by him?

And the other of the two conjectures, the twin prime conjecture, although he did not prove it.

But Tao Zhexuan and Zhang Yitang used his distribution deconstruction method?

Isn't that an indirect proof......

Therefore, Chen Zhou is confident that he will see a different scenery on the road of Gechai.

Moreover, in recent decades, Gechai has been lonely for too long.

Chen Zhou must let the world re-understand this Goldbach conjecture that haunts the dreams of Chinese people.

As for the so-called, existing tools, they can't solve the problem of Gochai.

Some kind of revolutionary new idea had to be introduced for it to be possible to solve the problem of Gochai.

For Chen Zhou, it is not difficult.

It is very likely that the good results of distribution deconstruction will be transferred from Crummel's theorem, Jepov's theorem, and twin prime theorem to Goldbach's conjecture.

Anyway, Chen Zhou now feels more and more that Ge guessing this is just a mathematical conjecture that he feels is almost the time, and chooses it as the topic.

In fact, it has a greater significance.

Regardless of Chen Zhou's confidence, he will be able to solve Gechai in the end.

But what if it's solved?

That is not to say, even if many people are not interested in and do not want to spend time on mathematical puzzles.

In fact, there are also different scenery?

Does it mean that Chen Zhou has the potential to change some people's minds?

It may have some subtle impact on the current mathematical community.

Retracting his thoughts, Chen Zhou began to write above the horizontal line he had just drawn:

[Any sufficiently large even number can be expressed as a number with no more than a number of prime factors, and the sum of another number with no more than b prime factors, which is recorded as "a+b". 】

This is the proposition about the strong Goldbach conjecture, that is, the proposition of the Gochai conjecture.

The "1+2" proved by Mr. Chen is true, that is, "any sufficiently large even number can be expressed as the sum of two numbers, one of which is a prime number, the other may be a prime number, and it may be the product of two prime numbers".

This is also the result of Mr. Chen's application of the large sieve method to the extreme.

This result is known as the "Chan theorem".

Looking at the words "Chen's theorem" that I wrote.

Chen Zhou smiled for no reason.

This Chen is not the other Chen.