NOVEL NEXT Xueba starts with change
Chapter 426 4 Ways
Chapter 426 Four Ways
Draw a circle on "Chen's Theorem".
Chen Zhou was thinking, maybe one day, maybe it won't be long.
"Chen's Theorem" becomes the full Goldbach's Theorem.
Of course, in a sense, Goldbach's theorem can also be called "Chen's theorem".
As for this "Chen", it is naturally Chen Zhou's Chen.
Withdrawing this distant thought, Chen Zhou focused his attention on Goldbach's conjecture again.
Judging from the previous research, there are four ways to study Gechai.
They are almost prime numbers, exceptional sets, the three prime number theorem for small variables, and almost Goldbach's problem.
An almost prime number is a positive integer with a small number of prime factors.
Suppose N is an even number, although it cannot prove that N is the sum of two prime numbers, it is enough to prove that it can be written as the sum of two almost prime numbers.
That is A+B.
Among them, the number of prime factors of A and B is not too many.
That is what Chen Zhou just wrote, the proposition I guessed.
The latest development of the "a+b" proposition is Mr. Chen's "1+2".
As for the "1+1" of the ultimate mystery, it is far away.
The progress in the direction of almost prime numbers is obtained by using the sieve method.
However, Mr. Chen used the sieve method to the extreme, and he just stayed on the "1+2".
Therefore, many mathematicians also believe that it is difficult to break through Mr. Chen's application of the sieve method in current research.
This is also the biggest reason why research in this direction has stagnated for such a long time.
Before finding a more reasonable tool, or in other words, a tool that can further play the role of the screening method.
The proof of "1+1" will never have a major breakthrough.
Chen Zhou also agrees with this point of view.
However, how easy is it to break through a tool that has been used to the extreme?
For a mature mathematical tool, the introduction of new mathematical ideas will also become more difficult.
But fortunately, when Chen Zhou was studying Kramer's conjecture, more or less, intentionally or unintentionally, he came up with the distribution structure method.
The original distribution structure method is a tool that combines mathematical ideas such as the sieve method and the circle method.
Therefore, in Chen Zhou's thinking, the key point for him to break through the limitations of the big sieve method lies in the distribution structure method.
On the draft paper, Chen Zhou wrote the distribution structure method separately on the right.
The method for almost prime numbers is on the left.
Below the almost prime method is the exception set.
The so-called exception set refers to taking a fixed large integer x on the number axis.
Then look forward from x to find those even numbers that make Goldbach's conjecture invalid.
These even numbers are called exceptional even numbers.
The key to this idea is that no matter how big x is, as long as x is before, there is only one exceptional even number.
And the even number of this exception is 2, that is, only 2 makes the guess wrong.
And 2, everyone understands.
Then, it can be shown that the density of these exceptional even numbers is zero.
It also proves that Goldbach's conjecture is true for almost all even numbers.
The research on this line of thought may not be so well-known in China.
But from the perspective of the world, as soon as Vinogradov's three prime number theorem was published, four proofs appeared at the same time on the way of exception sets.
Among them, Mr. Hua Lao's famous theorem is included.
An interesting thing to say is.
Folks, people often claim that they have proved that Goldbach's conjecture is correct in the sense of probability.
But in fact, they just "prove" that the exceptional even number is zero density.
As for the conclusion...
Mr. Hua had really proved it as early as 60 years ago.
So, sometimes I really can't listen to Minke's bluffing.
Take Chen Zhou himself as an example, if he cares about the voices of the minkes.
Then, the emails from those civil servants who filled the mailbox are really big enough for him.
"If Goldbach's conjecture for even numbers is correct, then the conjecture for odd numbers is also correct..."
After the third research approach "The Three Prime Number Theorem of Small Variables", Chen Zhou began to think and write down the research ideas of this approach.
[It is known that the odd number N can be expressed as the sum of three prime numbers. If it can be proved that one of the three prime numbers is very small...]
On this path, the person who has been researching is Mr. Pan, a famous mathematician in Huaguo.
If the first prime number can always be 3, then it proves my guess.
Following this idea, Mr. Pan began to study the three prime number theorem with a small prime variable when he was 25 years old.
This small prime variable does not exceed N to the θ power.
The research goal is to prove that θ can be 0.
That is to say, this small prime variable is bounded, so the Goldbach's conjecture of even numbers is introduced.
Mr. Pan first proved that θ can be 1/4.
Unfortunately, subsequent work in this area has not progressed.
Until the 90s, Professor Zhan Tao pushed Mr. Pan's theorem to 7/200.
Although this number is relatively small.
But it's still greater than 0.
Judging from the research history of the above three approaches, the contributions of Huaguo mathematicians in this area can be said to be outstanding.
It's just that no one can finally solve this problem that has plagued mathematicians for nearly 300 years.
Moreover, it is because of the research of these mathematicians that Goldbach's conjecture has extraordinary significance in the mathematics circles of Huaguo, even Huaguo.
On the draft paper, Chen Zhou sorted out his research ideas and wrote down his thoughts.
For his distribution structure method, Chen Zhou already had an extraordinary idea.
This method, which combines many mathematical ideas, has also placed more expectations on Chen Zhou.
After sorting out the "Three Prime Number Theorem for Small Variables", Chen Zhou glanced at the blank space on the draft paper.
Fortunately, he drew the previous horizontal line relatively low.
These sorted and compressed essences are able to stand on this piece of white paper.
After stretching, Chen Zhou looked at the time, and it was only after 10 o'clock in the evening.
Since it's still early, let's get on with it!
Thinking in this way, Chen Zhou began to sort out the "almost Goldbach problem".
The "Almost Goldbach Problem" was first researched by Linnik in a 1953-page paper in 70.
Linick proved that there exists a fixed non-negative integer k such that any large even number can be written as the sum of two prime numbers and k powers of 2.
Some people say that this theorem seems to uglify Goldbach's conjecture.
But in fact, it has a very profound meaning.
It can be noticed that the integers that can be written as the sum of k powers of 2 form a very sparse set.
That is to say, for any given x, the number of such integers in front of x will not exceed the kth power of logx.
Therefore, Linick's theorem points out that although we can't prove Goldbach's conjecture, we can find a very sparse subset in the set of integers.
Every time from this sparse subset, an element is pasted into the expression of these two prime numbers, and this expression is established.
The k here is used to measure the degree of approximation to Goldbach's conjecture.
The smaller the value of k, the closer it is to Goldbach's conjecture.
Then, it is obvious that if k is equal to 0.
Almost powers of 2 in Goldbach's problem no longer appear.
Thus, Linick's theorem becomes Goldbach's conjecture.
Thanks to the book friend Tudou for the 4000 starting coins rewarded by sickness!
Well, the students were not motivated to build the building at all, so he just evacuated the building...
(End of this chapter)
Draw a circle on "Chen's Theorem".
Chen Zhou was thinking, maybe one day, maybe it won't be long.
"Chen's Theorem" becomes the full Goldbach's Theorem.
Of course, in a sense, Goldbach's theorem can also be called "Chen's theorem".
As for this "Chen", it is naturally Chen Zhou's Chen.
Withdrawing this distant thought, Chen Zhou focused his attention on Goldbach's conjecture again.
Judging from the previous research, there are four ways to study Gechai.
They are almost prime numbers, exceptional sets, the three prime number theorem for small variables, and almost Goldbach's problem.
An almost prime number is a positive integer with a small number of prime factors.
Suppose N is an even number, although it cannot prove that N is the sum of two prime numbers, it is enough to prove that it can be written as the sum of two almost prime numbers.
That is A+B.
Among them, the number of prime factors of A and B is not too many.
That is what Chen Zhou just wrote, the proposition I guessed.
The latest development of the "a+b" proposition is Mr. Chen's "1+2".
As for the "1+1" of the ultimate mystery, it is far away.
The progress in the direction of almost prime numbers is obtained by using the sieve method.
However, Mr. Chen used the sieve method to the extreme, and he just stayed on the "1+2".
Therefore, many mathematicians also believe that it is difficult to break through Mr. Chen's application of the sieve method in current research.
This is also the biggest reason why research in this direction has stagnated for such a long time.
Before finding a more reasonable tool, or in other words, a tool that can further play the role of the screening method.
The proof of "1+1" will never have a major breakthrough.
Chen Zhou also agrees with this point of view.
However, how easy is it to break through a tool that has been used to the extreme?
For a mature mathematical tool, the introduction of new mathematical ideas will also become more difficult.
But fortunately, when Chen Zhou was studying Kramer's conjecture, more or less, intentionally or unintentionally, he came up with the distribution structure method.
The original distribution structure method is a tool that combines mathematical ideas such as the sieve method and the circle method.
Therefore, in Chen Zhou's thinking, the key point for him to break through the limitations of the big sieve method lies in the distribution structure method.
On the draft paper, Chen Zhou wrote the distribution structure method separately on the right.
The method for almost prime numbers is on the left.
Below the almost prime method is the exception set.
The so-called exception set refers to taking a fixed large integer x on the number axis.
Then look forward from x to find those even numbers that make Goldbach's conjecture invalid.
These even numbers are called exceptional even numbers.
The key to this idea is that no matter how big x is, as long as x is before, there is only one exceptional even number.
And the even number of this exception is 2, that is, only 2 makes the guess wrong.
And 2, everyone understands.
Then, it can be shown that the density of these exceptional even numbers is zero.
It also proves that Goldbach's conjecture is true for almost all even numbers.
The research on this line of thought may not be so well-known in China.
But from the perspective of the world, as soon as Vinogradov's three prime number theorem was published, four proofs appeared at the same time on the way of exception sets.
Among them, Mr. Hua Lao's famous theorem is included.
An interesting thing to say is.
Folks, people often claim that they have proved that Goldbach's conjecture is correct in the sense of probability.
But in fact, they just "prove" that the exceptional even number is zero density.
As for the conclusion...
Mr. Hua had really proved it as early as 60 years ago.
So, sometimes I really can't listen to Minke's bluffing.
Take Chen Zhou himself as an example, if he cares about the voices of the minkes.
Then, the emails from those civil servants who filled the mailbox are really big enough for him.
"If Goldbach's conjecture for even numbers is correct, then the conjecture for odd numbers is also correct..."
After the third research approach "The Three Prime Number Theorem of Small Variables", Chen Zhou began to think and write down the research ideas of this approach.
[It is known that the odd number N can be expressed as the sum of three prime numbers. If it can be proved that one of the three prime numbers is very small...]
On this path, the person who has been researching is Mr. Pan, a famous mathematician in Huaguo.
If the first prime number can always be 3, then it proves my guess.
Following this idea, Mr. Pan began to study the three prime number theorem with a small prime variable when he was 25 years old.
This small prime variable does not exceed N to the θ power.
The research goal is to prove that θ can be 0.
That is to say, this small prime variable is bounded, so the Goldbach's conjecture of even numbers is introduced.
Mr. Pan first proved that θ can be 1/4.
Unfortunately, subsequent work in this area has not progressed.
Until the 90s, Professor Zhan Tao pushed Mr. Pan's theorem to 7/200.
Although this number is relatively small.
But it's still greater than 0.
Judging from the research history of the above three approaches, the contributions of Huaguo mathematicians in this area can be said to be outstanding.
It's just that no one can finally solve this problem that has plagued mathematicians for nearly 300 years.
Moreover, it is because of the research of these mathematicians that Goldbach's conjecture has extraordinary significance in the mathematics circles of Huaguo, even Huaguo.
On the draft paper, Chen Zhou sorted out his research ideas and wrote down his thoughts.
For his distribution structure method, Chen Zhou already had an extraordinary idea.
This method, which combines many mathematical ideas, has also placed more expectations on Chen Zhou.
After sorting out the "Three Prime Number Theorem for Small Variables", Chen Zhou glanced at the blank space on the draft paper.
Fortunately, he drew the previous horizontal line relatively low.
These sorted and compressed essences are able to stand on this piece of white paper.
After stretching, Chen Zhou looked at the time, and it was only after 10 o'clock in the evening.
Since it's still early, let's get on with it!
Thinking in this way, Chen Zhou began to sort out the "almost Goldbach problem".
The "Almost Goldbach Problem" was first researched by Linnik in a 1953-page paper in 70.
Linick proved that there exists a fixed non-negative integer k such that any large even number can be written as the sum of two prime numbers and k powers of 2.
Some people say that this theorem seems to uglify Goldbach's conjecture.
But in fact, it has a very profound meaning.
It can be noticed that the integers that can be written as the sum of k powers of 2 form a very sparse set.
That is to say, for any given x, the number of such integers in front of x will not exceed the kth power of logx.
Therefore, Linick's theorem points out that although we can't prove Goldbach's conjecture, we can find a very sparse subset in the set of integers.
Every time from this sparse subset, an element is pasted into the expression of these two prime numbers, and this expression is established.
The k here is used to measure the degree of approximation to Goldbach's conjecture.
The smaller the value of k, the closer it is to Goldbach's conjecture.
Then, it is obvious that if k is equal to 0.
Almost powers of 2 in Goldbach's problem no longer appear.
Thus, Linick's theorem becomes Goldbach's conjecture.
Thanks to the book friend Tudou for the 4000 starting coins rewarded by sickness!
Well, the students were not motivated to build the building at all, so he just evacuated the building...
(End of this chapter)
Tip: You can use left, right, A and D keyboard keys to browse between chapters.