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Chapter 425 This Chen is not that Chen
Chapter 425 This Chen is not that Chen
Goldbach's conjecture originally stated that any integer greater than 2 can be written as the sum of three prime numbers.
Later, because of the cash mathematics prize, the convention "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 statement 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.
Consider starting from n>5.
When n is an even number, n=2+(n-2), n-2 is also an even number, 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, which can be decomposed into the sum of two prime numbers.
This is also known as "Jon Goldbach's conjecture", or "Goldbach's conjecture about even numbers".
While thinking, Chen Zhou recorded some necessary content on the draft paper.
For the study of mathematical conjectures, the formulation of conjectures, and the formulation of conjectures.
It is the first and most important step.
Habitually tapped the draft paper with a pen, Chen Zhou left a space in the middle of the draft paper, and then drew a horizontal line.
Below the horizontal line, Chen Zhou wrote the seven words "Weak Goldbach Conjecture".
Then, Chen Zhou continued to write some content about the weak Goldbach conjecture on the draft paper.
The so-called "weak Goldbach conjecture" is derived from the "strong Goldbach conjecture".
Its statement is "Any odd number greater than 7 can be written as the sum of three prime numbers".
As for the "strong and weak points", if the "strong Goldbach's conjecture" is established, then the "weak Goldbach's conjecture" must be established.
In contrast, the difficulty of the two is not the same.
Between 2012 and 2013, Peruvian mathematician Harold Hoofgot published two papers announcing a thorough proof of the weak Goldbach conjecture.
Then, Hoofgot's colleagues also used a computer to verify the proof process.
Therefore, the weak Goldbach's conjecture derived from the strong Goldbach's conjecture was finally solved first.
However, the latest research results of Jan Goldbach's conjecture still rest on the detailed proof of "1973+1" published by Mr. Chen in 2.
After that, there was little progress on the Jan Goldbach conjecture.
Although in 2002, someone made something.
However, it is difficult to say that it is substantial progress.
As for the proof of the weak Goldbach conjecture, the corresponding results have not been translated to the strong Goldbach conjecture.
Regarding this point, Chen Zhou remembered that Tao Zhexuan seemed to have said it.
A basic technique for studying the weak Goldbach conjecture is the method of Hardy-Littlewood and Vinogradov.
It is unlikely that it can be used in the strong Goldbach conjecture.
The research on Jan Goldbach's conjecture is basically limited to the category of analytic number theory.
Chen Zhou has also studied the method of weak Goldbach's conjecture proof, including the basic technology.
He quite agrees with Terence Tao's point of view.
This is why Jan Goldbach's conjecture is difficult.
On the one hand, everyone can't seem to find, any new tools.
On the other hand, it seems that its links with other areas of mathematics are very weak at present.
It is difficult to leverage strength.
In contrast, for the Riemann Hypothesis, there are some new discoveries almost every few years.
Moreover, some of these discoveries are based on operator theory, some are based on non-commutative geometry, and some are still based on analytic number theory.
And, from time to time, some mathematicians will excitedly announce that they have proved the Riemann Hypothesis.
Such a comparison, in fact, creates a dilemma in the study of Goldbach's conjecture.
That is, there are really not many mathematicians who are really committed to doing it.
Mathematics research, including physics research, is actually all about youth.
Most of the mathematical and physical achievements were made when the researchers were young.
Therefore, for Brother Guess, a mathematical conjecture that is difficult to produce results.
Most mathematicians are unwilling to take this lonely, youth-consuming Shura road.
Speaking of it, there is another very embarrassing reason.
After gradually reducing the number of people who study Gechai.
Go out to an academic conference and you'll find that there's no one to discuss ideas with.
Of course, Chen Zhou dared to walk such a lonely path of Shura.
For him, isn't the previous Krammel conjecture also known as "no one can come close to the proof"?
But in the end, didn't he turn it into Krammel's theorem?
Didn't the Jebov conjecture, which is known as one of the two most important conjectures in the prime number interval problem, also be proved by him?
And the other of the two major conjectures, the twin prime number conjecture, although he did not prove it.
But Tao Zhexuan and Zhang Yitang used his distribution deconstruction method?
It's almost like indirect proof...
Therefore, Chen Zhou is confident that he will see different scenery on the road of Gechai.
Moreover, in recent decades, Brother Chai has been lonely for too long.
Chen Zhou must let the world re-understand this Goldbach's conjecture that haunts the Chinese people.
As for the so-called, the existing tools cannot solve this problem.
Some kind of revolutionary new idea must be introduced before it is possible to solve Ge Chai.
For Chen Zhou, it was not difficult.
The good results obtained by the distribution deconstruction method are likely to translate from Krammel's theorem, Jebov's theorem and twin prime number theorem to Goldbach's conjecture.
In any case, Chen Zhou felt more and more now that my brother guessed this was just a mathematical conjecture that he felt that it was almost time, so he chose it as a topic.
In fact, it has more significance.
Regardless of Chen Zhou's confidence, he can finally solve Brother Guess.
But what if it is solved?
That is to say, even though many people are not interested in, and are not willing to spend time on difficult mathematical problems.
In fact, there is a different scenery?
Does it mean that Chen Zhou may change some people's minds?
It may have some subtle effects on the current mathematics world.
Withdrawing his thoughts, Chen Zhou began to write above the horizontal line drawn just now:
[Any sufficiently large even number can be expressed as the sum of a number whose number of prime factors does not exceed a, and another number whose number of prime factors does not exceed b, which is recorded as "a+b". 】
This is the proposition about the strong Goldbach conjecture, that is, the proposition of Ge Guess.
And 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, or it may be two prime numbers product of ".
This is also the result of Mr. Chen's extreme application of the big sieve method.
This result is called "Chen's theorem".
Look at the four words "Chen's Theorem" that I wrote down.
Chen Zhou smiled for no reason.
This Chen is not that Chen.
(End of this chapter)
Goldbach's conjecture originally stated that any integer greater than 2 can be written as the sum of three prime numbers.
Later, because of the cash mathematics prize, the convention "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 statement 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.
Consider starting from n>5.
When n is an even number, n=2+(n-2), n-2 is also an even number, 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, which can be decomposed into the sum of two prime numbers.
This is also known as "Jon Goldbach's conjecture", or "Goldbach's conjecture about even numbers".
While thinking, Chen Zhou recorded some necessary content on the draft paper.
For the study of mathematical conjectures, the formulation of conjectures, and the formulation of conjectures.
It is the first and most important step.
Habitually tapped the draft paper with a pen, Chen Zhou left a space in the middle of the draft paper, and then drew a horizontal line.
Below the horizontal line, Chen Zhou wrote the seven words "Weak Goldbach Conjecture".
Then, Chen Zhou continued to write some content about the weak Goldbach conjecture on the draft paper.
The so-called "weak Goldbach conjecture" is derived from the "strong Goldbach conjecture".
Its statement is "Any odd number greater than 7 can be written as the sum of three prime numbers".
As for the "strong and weak points", if the "strong Goldbach's conjecture" is established, then the "weak Goldbach's conjecture" must be established.
In contrast, the difficulty of the two is not the same.
Between 2012 and 2013, Peruvian mathematician Harold Hoofgot published two papers announcing a thorough proof of the weak Goldbach conjecture.
Then, Hoofgot's colleagues also used a computer to verify the proof process.
Therefore, the weak Goldbach's conjecture derived from the strong Goldbach's conjecture was finally solved first.
However, the latest research results of Jan Goldbach's conjecture still rest on the detailed proof of "1973+1" published by Mr. Chen in 2.
After that, there was little progress on the Jan Goldbach conjecture.
Although in 2002, someone made something.
However, it is difficult to say that it is substantial progress.
As for the proof of the weak Goldbach conjecture, the corresponding results have not been translated to the strong Goldbach conjecture.
Regarding this point, Chen Zhou remembered that Tao Zhexuan seemed to have said it.
A basic technique for studying the weak Goldbach conjecture is the method of Hardy-Littlewood and Vinogradov.
It is unlikely that it can be used in the strong Goldbach conjecture.
The research on Jan Goldbach's conjecture is basically limited to the category of analytic number theory.
Chen Zhou has also studied the method of weak Goldbach's conjecture proof, including the basic technology.
He quite agrees with Terence Tao's point of view.
This is why Jan Goldbach's conjecture is difficult.
On the one hand, everyone can't seem to find, any new tools.
On the other hand, it seems that its links with other areas of mathematics are very weak at present.
It is difficult to leverage strength.
In contrast, for the Riemann Hypothesis, there are some new discoveries almost every few years.
Moreover, some of these discoveries are based on operator theory, some are based on non-commutative geometry, and some are still based on analytic number theory.
And, from time to time, some mathematicians will excitedly announce that they have proved the Riemann Hypothesis.
Such a comparison, in fact, creates a dilemma in the study of Goldbach's conjecture.
That is, there are really not many mathematicians who are really committed to doing it.
Mathematics research, including physics research, is actually all about youth.
Most of the mathematical and physical achievements were made when the researchers were young.
Therefore, for Brother Guess, a mathematical conjecture that is difficult to produce results.
Most mathematicians are unwilling to take this lonely, youth-consuming Shura road.
Speaking of it, there is another very embarrassing reason.
After gradually reducing the number of people who study Gechai.
Go out to an academic conference and you'll find that there's no one to discuss ideas with.
Of course, Chen Zhou dared to walk such a lonely path of Shura.
For him, isn't the previous Krammel conjecture also known as "no one can come close to the proof"?
But in the end, didn't he turn it into Krammel's theorem?
Didn't the Jebov conjecture, which is known as one of the two most important conjectures in the prime number interval problem, also be proved by him?
And the other of the two major conjectures, the twin prime number conjecture, although he did not prove it.
But Tao Zhexuan and Zhang Yitang used his distribution deconstruction method?
It's almost like indirect proof...
Therefore, Chen Zhou is confident that he will see different scenery on the road of Gechai.
Moreover, in recent decades, Brother Chai has been lonely for too long.
Chen Zhou must let the world re-understand this Goldbach's conjecture that haunts the Chinese people.
As for the so-called, the existing tools cannot solve this problem.
Some kind of revolutionary new idea must be introduced before it is possible to solve Ge Chai.
For Chen Zhou, it was not difficult.
The good results obtained by the distribution deconstruction method are likely to translate from Krammel's theorem, Jebov's theorem and twin prime number theorem to Goldbach's conjecture.
In any case, Chen Zhou felt more and more now that my brother guessed this was just a mathematical conjecture that he felt that it was almost time, so he chose it as a topic.
In fact, it has more significance.
Regardless of Chen Zhou's confidence, he can finally solve Brother Guess.
But what if it is solved?
That is to say, even though many people are not interested in, and are not willing to spend time on difficult mathematical problems.
In fact, there is a different scenery?
Does it mean that Chen Zhou may change some people's minds?
It may have some subtle effects on the current mathematics world.
Withdrawing his thoughts, Chen Zhou began to write above the horizontal line drawn just now:
[Any sufficiently large even number can be expressed as the sum of a number whose number of prime factors does not exceed a, and another number whose number of prime factors does not exceed b, which is recorded as "a+b". 】
This is the proposition about the strong Goldbach conjecture, that is, the proposition of Ge Guess.
And 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, or it may be two prime numbers product of ".
This is also the result of Mr. Chen's extreme application of the big sieve method.
This result is called "Chen's theorem".
Look at the four words "Chen's Theorem" that I wrote down.
Chen Zhou smiled for no reason.
This Chen is not that Chen.
(End of this chapter)
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