When the candidates did not make it to the final game of the national finals, the pressure was actually not huge.

They are selected by the school, and then the provincial preliminary and preliminary rounds, and then they can participate in the CMO competition...... After experiencing the difficulty of the first half, the psychological pressure on them in the second half of the game has become even greater.

This is the highest level of mathematics in China, everyone wants to stand out in such an event, and after deducting those candidates who have been eliminated, you can imagine how much pressure is superimposed on them.

Especially for the provinces and cities that have been winning generals in the past, this kind of pressure is far more terrible than others.

Hubei, Beijing, Zhejiang, Guangdong and other places.

The one who collapsed just now was a sophomore in Guangdong, there was no way, he couldn't solve any of the three questions for more than two hours, which made his mood suddenly break the balance, and the whole person collapsed.

There must be psychologists, and there is more than one, these candidates are the future pillars of the motherland, and they can't let them go wrong easily.

Soon, a professional psychological counselor went to enlighten the candidates just now.

And just three minutes later, one of the test takers collapsed again.

"Oh no, this candidate is foaming at the mouth, doctor, doctor!"

This time, it's not psychological pressure, it's a physical problem.

In the field of the national final, the situation is frequent, especially in recent years, the candidate's psychological and physical quality to resist pressure is getting weaker and weaker, and even run away from home at every turn or directly depressed, and in serious cases, they directly open the window to make a leap in class.

So that in these years, even the pressure on teachers is getting bigger and bigger, you can't beat, you can't scold, you can't scold if you go too far, you can even be considered corporal punishment of students, and now the Internet is transparent, if you really want to do something, the masses who don't know the truth will doxx you, put things on the bright side, and many teachers have suffered from the troubles of life.

In the past, there have been few cases of beating students with a ring ruler in recent years.

However, in Fang Chao's view, a certain punishment may not be a good thing for students, and too much smooth sailing will make people's mentality too fragile.

Fang Chao ignored these people, and instead started to do the third question on his own.

This third question is a bit interesting.

The title is purple: let the integer n≥3, there are k primes not exceeding n, let A be a subset of the set {2,3,......,n}, the number of elements of A is less than k, and any number in A is not a multiple of another number,

Proof: There is a k-element subset B of the set {2,3,......,n} such that any number in B is not a multiple of the other, and B contains A.

This question is about prime numbers.

Very interesting.

Prime numbers are also known as prime numbers.

According to the fundamental theorem of arithmetic, every integer greater than 1 is either a prime number in itself or can be written as the product of a series of prime numbers, and the written form is unique if the order of these prime numbers in the product is not taken into account. The smallest prime number is 2.

To date, no formula has been found to find all prime numbers.

So far, it has been found that the largest prime number is 22.33 million digits, and if it were printed in ordinary font size, it would be more than 65 kilometers long.

This represents the infinite possibilities of prime numbers.

He was able to give a lot of trouble in mathematics, but he also made mathematicians happy.

Countless conjectures have been born from this.

For example, if a twin prime is a pair of prime numbers with a difference of 2, such as 11 and 13, is there an infinite number of twin primes? This is also a very famous conjecture, the twin prime conjecture.

Or is there an infinite number of primes in the Fibonacci sequence? Is there an infinite number of Mersenne primes? Is there a prime number every n between n2 and (n+1)2? Is there an infinite form such as X2+1 prime?

and the most famous Goldbach conjecture.

About 270 years ago, Goldbach wrote a letter to Euler, as we all know, in the past, technology was not developed enough, at that time you can't expect to have QQ and WeChat, right? Of course, there was not even a phone call at that time.

It is in that situation, if you want to make friends, then you have to write a letter, everyone is very strange, and very mysterious, the earliest boyfriend and girlfriend have a love for the words will first have a letter exchange, the content of the heart is still very subtle at that time, not explicit at all, about a month or so of correspondence exchange will be proposed to meet, we can talk about the formal relationship in the future, talk about it and break the letter, we have no common topic.

As a German mathematician, Goldbach was a smart man, and it was not easy to become a pen pal with him.

Mathematicians are arrogant and lonely, but they are also extremely proud, if you want to be recognized, then you must at least be on par with me in mathematics, right? Otherwise, isn't it embarrassing that everyone can't talk about it in the future?

Mathematicians play letters with people? Are you in a hurry?

Besides, there were really too few mathematicians at that time, and there were pitiful few.

So, in a special environment, Goldbach and Euler became pen pals, and this correspondence lasted for more than 30 years.

One day at dinner, Goldbach thought of a question, but he was so dizzy that he didn't come up with a reason, so he thought of his good friend Euler.

Then he wrote in the letter, "Brother Ora, I have a problem now, can you help me solve it?"

Take an odd number, such as 77, and write it as the sum of three prime numbers: 77 = 53 + 17 + 7;

Take an odd number, such as 461, 461 = 449 + 7 + 5, which is also the sum of three prime numbers, 461 can also be written as 257 + 199 + 5, which is still the sum of three prime numbers. In this way, I found that any odd number greater than 9 is the sum of three prime numbers.

But how can this be proven? Although every test ever done has yielded the above results, it is impossible to test all odd numbers, and what is needed is a general proof, not an individual test, right? Brother Ora, you're so smart, you can help me with it, right? ”

We have already said before, mathematicians are proud and arrogant, and Goldbach has already slapped all the sycophants, and all of them are slapped on the key points, the most important thing for a mathematician is to be affirmed by another mathematician, as his good friend, Euler must be sure of Goldbach's strength, even his little brother is demanding himself, how can he not let him down, right?

So he replied, "I agree with your proposition!" ”