"Gentlemen and ladies, this is the captain's announcement. I am the captain of this flight, Chen Baiqiang. I'm sorry to disturb your sweet dreams. Our flight will begin to descend soon. Please take a short rest and return as soon as possible.

Go back to your seat and fasten your seat belt."

"At the same time, thank you for your understanding, cooperation and support of our work all the way. In fact, for me, every flight is more or less the same, the same plan, the same flight."

"This flight is different. Our International Mathematics Olympiad Chinese National Team is on this flight. It is our crew's honor to be able to transport you. Here, on behalf of Air China, I and all the crew would like to express our best wishes to you all."

With the highest respect and the most sincere blessings, I wish the Chinese national team a successful start and a glorious return!"

When the plane was about to land, the captain's announcement sounded, and everyone else looked at the imo Chinese national team. Only then did they know that there was such a special team on the same flight as them. Many people couldn't help but send warm greetings.

applause.

"Come on guys!"

"China team, come on!"

"..."

Liu Yichen and others couldn't help but sit up straight. They felt very proud, and at the same time they also felt a greater sense of responsibility and pressure.

After the plane landed, under the leadership of the stewardess, Liu Yichen and the others were the first to get off the plane. Liu Yichen held the national flag. At this time, he felt that the national flag was so heavy, as heavy as a thousand pounds.

After getting off the plane, staff from the Chinese Embassy in Madrid came to the airport to pick them up in person. The two cars looked so cute and beautiful with small five-star red flags on the fronts. The deputy team leader thanked them one by one, and then Liu Yichen and the others got into the car.

in.

Half an hour later, we finally arrived at the arranged hotel. The team leader Xiong Bin and the deputy team leader hugged each other, and then took Liu Yichen and the other six people to check into the hotel. The organizer did not bear the travel expenses, only the expenses. However,

I have to say that the conditions of this hotel are really good. After everyone put their luggage in the room, they went to the leader's room.

Xiong Bin introduced the situation of this IMO. The opening ceremony will start on July 15th. They can use these days to adapt to the environment. The total number of participating countries and regions in this 49th International Olympiad Mathematics Competition will reach 109.

Hitting a record high again. Next, let everyone listen to the deputy team leader, because the team leaders from each country will form the main examination committee. The test questions and answers will be held by the participating countries. Each country will have 3-5 questions. The host country will form based on the test questions provided by other countries and regions.

The topic selection committee evaluates and preliminarily selects the test questions, thereby selecting 30 questions, and finally selects 6 questions as test questions. The exam is divided into two tests over two days, with 3 questions each, 4.5 hours per test, 7 points for each question, full score

42 points.

Next, Xiong Bin will participate in topic selection and translate the test papers into the Chinese language. Therefore, during this period, he cannot be with everyone, but will be responsible for the deputy team leader.

After Xiong Bin left, everyone went to have a good rest. This kind of jet lag was really tiring. Even Liu Yichen felt like he couldn't bear it when he went abroad for the first time.

Now that conditions in China allow, you can arrive early to adapt to the new environment. Many countries arrive the day before the opening ceremony, and not many people can bear the jet lag. This is reflected in the winning teams of previous Olympic Mathematics Competitions.

, this can be seen from the fact that China is the only one in the third world.

In the blink of an eye, the time has arrived on July 15th. The opening ceremony of the 49th IMO competition officially kicked off. 109 participating teams from all over the world gathered here. It can be said that these are the most outstanding mathematical geniuses from each country this year.

, everyone gathered together to participate in this grand event. The host warmly welcomed the arrival of participating teams from various countries, and some of the performances at the opening ceremony were also full of Spanish culture, allowing people to experience a unique foreign culture.

Spain is located on the Iberian Peninsula in southwest Europe, at the junction of Europe and Africa. It is bordered by the Bay of Biscay to the north, France to the northeast, and Morocco in Africa to the south across the Strait of Gibraltar. It is a mountainous country.

The total area is 506,000 people, because Spain was an important maritime power in the Age of Discovery in the 16th century. It once had the most powerful navy in the world with Portugal and was the maritime overlord in the 16th century. Therefore, Spanish is widely used around the world.

It is the second largest country in the world with Spanish as its official language, second only to English.

Therefore, Spain has a very unique culture, with unrestrained enthusiasm, love of bullfighting, and flamenco dance. It is also the hometown of guitar. Among the programs at the opening ceremony, there is a flamenco dance program.

Of course, there is also a performance called "Coca". This custom originated from a local legend in the Spanish Middle Ages. According to the local Spanish legend, two local women in the Middle Ages relied on this dance to escape the entanglement of the evil dragon and survive.

, "Koka" comes from this.

In the "Koka" performance, the little girls put on beautiful traditional costumes, and then let their mothers put them on their shoulders, and the mother and daughter danced together.

With the end of the opening ceremony, it also means that the 49th imo competition has begun. Unlike domestic competitions, you can bring any stationery and drawing tools to the imo competition. In addition, because the competition time is long, each player can bring their own food

Drinks are allowed into the venue, and no more than three reference books are allowed.

"Ding~~" Just when the competition was about to officially start, Liu Yichen was thinking about whether to bring reference materials, when the metallic voice of the system sounded in his mind, "Congratulations to the host, the math level has been improved from lv9 to lv10, the comprehensive evaluation level is s, and the reward

Proof paper of Zhou’s conjecture on host Mersenne prime numbers!”

Liu Yichen was startled. He didn't expect that Mathematics would be upgraded to level 10 at this time. He was immersed in the system interface:

a:Mathematics:lv10

b: Physics: lv8 (400/500)

c: Biology: lv8 (30/500)

d:Chemistry:lv8(50/500)

e: Chinese: lv5 (189/200)

f:English:lv5(180/200)

Points:2050

Lifespan in the upper left corner: 366 days

"I'm already at Level 10 in Mathematics. According to the system, I am the invincible among the top students in high school. Why should I bring any reference materials?" Liu Yichen muttered to himself, and he immediately made up his mind not to bring any materials.

"Captain, what materials do you plan to bring to the exam tomorrow?" Zhang Duanxiang asked.

"Me? I don't need to bring any information!" Liu Yichen said with a faint smile.

"No way, are you so sure?" Zhang Duanxiang was surprised: "Captain, if you do this, be careful of being beaten up by the team leader!"

"It's okay, imo, it's useless to bring reference materials for exams!" Liu Yichen shook his head and said: "Just like domestic exams, closed-book exams are never the most difficult. The most difficult thing is open-book exams, which make it difficult for you to check the information.

arrive."

Zhang Duanxiang looked at Liu Yichen suspiciously, but after thinking about it, he thought it made sense. In the previous IMO competitions, no one said that it would be useful to bring reference materials.

However, he also thought that not wearing one might seem too arrogant. If he lost the IMO gold medal, he would inevitably be scolded by the team leader and deputy team leader, so he thought it would be safer to bring one.

Liu Yichen lay on the bed, took out his computer, and began to search for Mersenne prime numbers.

Regarding Mersenne prime numbers, Zhou guessed that he had actually had some contact with them before, but the contact was not deep. He had only scratched the surface and had not even entered the door. He only knew that this thing existed.

But now it's different. After getting the proof paper of Mersenne's prime numbers and Zhou's conjecture, he must understand it deeply. Otherwise, he will submit the paper and need to answer the paper, but he will not be able to answer anything. This is very bad.

As he searched for information about Mersenne prime numbers, Liu Yichen also learned more about them. Mersenne prime numbers are an effective way to discover the largest known prime numbers. It promotes number theory research, and also promotes computational mathematics, programming technology, and network technology.

As well as the development of cryptography technology, the exploration of Mersenne prime numbers is more difficult. It not only requires advanced theory and proficient skills, but also requires arduous calculations.

As for its emergence, the history is relatively long. We have to move the time to the 17th century. At that time, French mathematician and founder of the French Academy of Sciences, Marin Mason, proposed a formula, that is, the positive integer of mp=2^p-1 is a prime number.

The exponent p is a prime number, and mp is a prime number. Because the proposer is Marin Mersenne, it is also called Mersenne prime number.

When p=2,3,5,7, mp are all prime numbers, but m11=2047=23×89 is not a prime number. Whether there are infinitely many Mersenne primes is one of the unsolved problems in number theory.

This kind of prime number is an important part of number theory research, and it is also one of the hot spots and difficulties in today's scientific exploration. Because the Mersenne prime number is rare and fascinating, it is known as the "diamond in number theory".

In the history of mathematics, there have been many amazing things about Mersenne prime numbers. For example, in 1772, when Euler was blind, he relied on mental arithmetic to prove that m31 was a prime number. It had 10 digits, which was very impressive at that time.

The largest known prime number in the world, he thus gained the reputation of a 'mathematical hero'. This was the precursor to the search for the largest known prime number. Euler also proved the converse of Euclid's theorem about perfect numbers, namely:

Every even perfect number has the form 2^p-1(2^p-1), where 2^p-1 is a prime number. This makes even perfect numbers completely a "by-product" of Mersenne prime numbers.

In 1883, the mathematician Povosin used Lucas's theorem to prove that m61 is also a prime number - this is what Mersenne missed. Mersenne also missed two other prime numbers: m89 and m107, which were discovered in 1911 and 1914 respectively.

Discovered by mathematician Bowers.

In the hundreds of years of exploration of Mersenne primes, countless mathematicians have invested in research, and Zhou's conjecture, or Zhou's conjecture, was cleverly formulated by the Chinese mathematician and linguist Zhou Haizhong based on the known Mersenne primes and their arrangements.

Using the contact observation method and incomplete induction method, he formally proposed a conjecture about the distribution of Mersenne prime numbers in February 1992, and gave the precise expression of its distribution for the first time. Later, this important conjecture was named '

Zhou's conjecture' or 'Zhou's conjecture'.

Its basic content is: when 2^(2^n)Chapter completed!