Volume 1: Student Life Chapter 425 This Chen is not that Chen
The Goldbach conjecture originally stated that any integer greater than 2 can be written as the sum of three prime numbers.
Later, because of cash mathematics prizes, the convention that "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 common conjecture statement 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 considering from n>5.
When n is an even number, n=2+(n-2), n-2 is also an even number and 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 on even numbers".
While thinking, Chen Zhou wrote down some necessary content on the draft paper.
Research on mathematical conjectures, the expression of conjectures, and the formalization of conjectures.
It is the first and most important step .
Chen Zhou habitually tapped the draft paper with a pen, left a blank 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".
The statement is "Any odd number greater than 7 can be written as the sum of three prime numbers."
As for the "distinction between strong and weak", if the "strong Goldbach conjecture" is true, then the "weak Goldbach conjecture" must be true.
Relatively speaking, the difficulty of the two is also different.
Between 2012 and 2013, Peruvian mathematician Harold Heofgot published two papers announcing the definitive proof of the weak Goldbach conjecture.
Later, Heofgot's colleagues also verified this proof process using computers.
Therefore, the weak Goldbach conjecture derived from the strong Goldbach conjecture was finally solved first.
The latest research results on the Strong Goldbach conjecture are still based on the detailed proof of "1+2" published by Mr. Chen in 1973.
After this, there was almost no progress on the Goldbach conjecture.
Although in 2002, someone did something.
However, it is hard to say that this is substantial progress.
As for the corresponding results of the proof of the weak Goldbach conjecture, they have not been transferred and applied to the strong Goldbach conjecture.
Chen Zhou remembered that Terence Tao seemed to have said this about this.
A basic technique for studying the weak Goldbach conjecture is the method of Hardy-Littlewood and Vinogradov.
It is unlikely to be used in the strong Goldbach conjecture.
The study of the Strong Goldbach conjecture is basically limited to the scope of analytic number theory.
Chen Zhou also studied the method of proving the weak Goldbach conjecture, including that basic technique.
He still quite agrees with Tao's point of view.
This is also the reason why the Goldbach conjecture is difficult.
On the one hand, people can't seem to find any new tools.
On the other hand, it currently seems that its connection with other fields of mathematics is very weak.
It is difficult to use the opponent's force to your advantage.
In contrast, there are some new discoveries about the Riemann hypothesis almost every few years.
Moreover, some of these discoveries are based on operator theory, some are based on non-commutative geometry, and some are based on analytic number theory.
Moreover, from time to time, some mathematicians will excitedly announce that they have proved the Riemann hypothesis.
This contrast actually creates a dilemma in the study of the Goldbach conjecture.
That is, there are really not many mathematicians who are really dedicated to doing it.
Mathematical research, including physics research, is actually a job for young people.
Most mathematical and physical achievements were proposed when the researchers were young.
Therefore, for a mathematical conjecture like the Goldbach conjecture, it is difficult to produce results.
Most mathematicians are unwilling to take this lonely, youth-consuming path.
There is another embarrassing reason.
The number of people studying Ge Guai is gradually decreasing.
Go out to an academic conference and you'll find that there's no one with whom you can discuss ideas.
Of course, Chen Zhou dares to take such a lonely Shura road.
For him, wasn’t the previous Cramer conjecture also known as “something that no one has come close to proving”?
But in the end, didn't he turn it into Cramer's theorem?
Wasn't he also able to prove the Jebov conjecture, one of the two most important conjectures in the prime number gap problem?
The other of the two major conjectures, the twin prime conjecture, was not proved by him.
But Terence Tao and Zhang Yitang used his distributed deconstruction method, right?
It's almost like indirect proof...
Therefore, Chen Zhou is confident that he will see different scenery on the road to Gechai.
Moreover, in recent decades, Ge Chai has been lonely for too long.
Chen Zhou must make the world re-recognize the Goldbach conjecture that has fascinated the Chinese people.
As for the so-called, existing tools cannot solve this problem.
Some revolutionary new idea must be introduced to solve the Ge guess.
It is not a difficult task for Chen Zhou.
The good results achieved by the distribution deconstruction method can very likely be transferred from Cramer's theorem, Gerbov's theorem and twin prime theorem to the Goldbach conjecture.
In any case, Chen Zhou now feels more and more that this guess is just a mathematical conjecture that he chose as the topic because he felt the time was almost right.
In fact, it has a more significant meaning.
Regardless of Chen Zhou's confidence, Ge Cai was eventually able to solve the problem.
But what if it is solved?
So can we say that even many people are not interested in and unwilling to waste time on difficult mathematical problems?
Are there actually different landscapes?
Does it mean that Chen Zhou may be able to change some people’s minds?
Perhaps it will have some subtle impact on the current mathematics community.
Recovering his thoughts, Chen Zhou began to write above the horizontal line he had just drawn:
[Any sufficiently large even number can be expressed as the sum of a number with no more than a prime factors and another number with no more than b prime factors, recorded as "a+b".]
This is the proposition about the strong Goldbach conjecture, also known as the Goldbach conjecture.
What Mr. Chen proved about "1+2" 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, and the other may be a prime number, or may be the product of two prime numbers."
This is also the result obtained by Mr. Chen when he applied the large screening method to the extreme.
This result is called "Chen's Theorem".
Looking at the four words "Chen's Theorem" that I wrote.
Chen Zhou smiled for no reason.
This Chen is not that Chen.
