Chapter 12 Twin Prime Conjecture and CMO Finals On Sunday afternoon, winter camp students from all over the country arrived at Jiangzhou University. Local students from Jiangzhou joined the Jiangyang Province team. The hotel run by Jiangzhou University was left entirely to the participating students. The students will be sent by teachers from major training institutions. Zou Yao brought six students including Lu Shan to Jiangzhou University. Of course Su Ming was not in it. Su Ming came with the Jiangyang Provincial Team. Lu Shan was a little surprised. When Zou Yao was doing the test that day, he clearly stated that only students with a score of 20 or above could enter the winter camp. Lu Shan didn't believe that all six students in the training class scored 20 points. Lu Shan looked at Zou Yao, and Zou Yao laughed awkwardly.
Lu Shan understood immediately. There is no limit on the number of places. This is all about money! The purpose of training institutions is to make money. They train you and also make money from you. Parents paid tens of thousands of yuan for training, but if they can't even get the qualification for the winter camp, won't they be furious? As for how the training institutions operate, only God knows. This winter camp has 31 participants from 650 provinces across the country, which is a record high. Because the five days are completely closed, Zou Yao cannot accompany everyone. Before leaving, Zou Yao called Lu Shan to his side alone. "Lu Shan, thank you! You reminded me that day. I have sorted out my thesis these days, and it should be no problem for it to be successful." Zou Yao took out a notebook from his bag and handed it to Lu Shan: "This is the knowledge points and some examples related to the CMO finals that I compiled this year. It's out of print! You should take a good look at it tonight." "Take the test well, I believe you will have no problem getting the gold medal!" Lu Shan gladly accepted it, "Thank you, Teacher Zou." Zou Yao looked at Lu Shan, as if he was looking at himself when he was young and participating in competitions, loving mathematics and being full of passion and ideals. But everything will be smoothed out by time. Zou Yao said: "The road of mathematics is not easy to walk. Now that I like it, I will stick to it!" Lu Shan nodded, Zou Yao was a good person. After the roll call at the winter camp in the evening, we randomly drew our own numbers. The number is not only used for grouping, but also serves as the admission ticket number for the final exam tomorrow and the day after tomorrow. After a simple opening ceremony, the students got to know each other and communicated in a relatively relaxed atmosphere. Lu Shan clearly felt the gap, which was in conversation, dress and knowledge. Among the 650 people, more than 70% are from developed cities such as Yanjing, Shanghai, and Yangcheng. Students in these places dress fashionably, feel relaxed and confident.
They truly treat winter camp as winter camp, coming here to enjoy and learn from the experience. On the contrary, most of the students who came from inland cities such as Jiangyang Province and even remote cities were timid and had no confidence, as if they came just for the exam. After being divided into groups, most of the groups began to communicate with outstanding students from Shanghai or Yenching University. Lu Shan was in the third group. Forty or fifty students surrounded Quan Kai, a senior student from Yanjing No. 3 Middle School. Quan Kai is handsome and he ranked in the top 10 in the National Mathematics League in September. His goal for this winter camp is to join the national training team. In contrast, Lu Shan's score was fifth in Jiangzhou City, and outside the top 500 in the country. Quan Kai said: "Let N = p1×p2×...×pn. If N+1 is a prime number, then N+1 must be greater than p1, p2,..., pn, so it is not in the set of assumed prime numbers..." Quan Kai was talking about the twin prime conjecture in number theory. 孪生素数就是指相差2的素数对，例如3和5，5和7，11和13…。 Expressed mathematically, there are infinite prime numbers p such that p + 2 is a prime number, and the prime number pair (p, p + 2) is called twin prime numbers. Mathematicians believe that this conjecture is correct, but have never been able to prove it. Lu Shan smiled. It is now 07 and the twin prime conjecture has not been proved. But he was reborn, and even without the help of Poincare, he knew that the twin prime conjecture had been proved. Among them, mathematician Tang Yi played an important role and made a major breakthrough in 2013. It was proved that there are infinite pairs of prime numbers whose difference is less than 7000. Later, this number was reduced to 246, and further progress was difficult until a few years before Lu Shan's death. Quan Kai said: "But we cannot prove it completely. Professor Tang Yi is an expert in this field and has been researching it for more than ten years. I am lucky enough to have met him. He will give a lecture on this topic tomorrow afternoon. Everyone can listen carefully." "We come to the winter camp, and participating in the finals is secondary. The most important thing is to communicate with each other, listen to the academic reports of experts and professors, and experience the wonders of the world of mathematics." Of course Lu Shan would not miss such a good opportunity to earn points. Lu Shan said: "It can be proved, but there are some minor problems." As soon as these words were spoken, everyone in the group looked at Lu Shan, thinking that this kid was bragging. Quan Kai was speaking proudly, when suddenly everyone's attention was focused on Lu Shan. Quan Kai looked Lu Shan up and down and frowned. Lu Shan's dress was too simple, a gray-black cotton coat, black cotton trousers, and velvet cloth shoes. It is obvious that these students are from backward areas. Students from big cities all wear down jackets, so who would wear cotton coats, especially when the cotton coats fade? Students from backward areas usually adopt the tactic of doing a large number of questions, and they finally enter the winter camp after doing countless questions. They may not even know what the twin prime conjecture is. Quan Kai felt that his speech had been challenged, so he stood up and said, "Do you know what the twin prime conjecture is?" Quan Kai: "This conjecture was proposed by Hilbert in his report at the International Congress of Mathematicians in 1900!" "Oh, you probably don't even know who Hilbert is."
"In large numbers, the interval between two primes is about times the number of digits, but 'twin' primes often appear in clusters, such as 3 and 5 and 11 and 13, whose difference is only 2." "The top mathematicians haven't proved it yet, and you're just saying you can prove it. You're so ignorant!" They are all the best high school students in various places, but no matter how good their math scores are, they are still high school students. They are competitive and want to show themselves. Many students were also very interested in the twin prime conjecture and had done research on it. They all said, "That's right, no one has been able to prove it yet. Did you hear the wrong topic?" "If you can prove the twin prime conjecture, why would you attend the CMO winter camp? Go get the Fields Medal!" The students laughed. Lu Shan smiled and didn't get angry. Instead, he took out a piece of chalk and wrote on the blackboard: "Bounded distance between prime numbers." Then Lu Shan continued to talk while writing down the inferences. New and old friends, please follow me and vote! (End of this chapter)