In modern China, the Chinese people are most familiar with the problems and conjectures in the mathematical world, the Goldbach conjecture, Xu Chi's reportage shocked the whole of China, and since then it has gone to the public with Mr. Chen Jingrun, who proved the Goldbach conjecture 1+2.

Junxin wanted to meet Mr. Chen a long time ago, and when he was teaching at USTC, he had this intention, but because of the time arrangement, Junxin did not make the trip and returned to Beijing. Later, because of various things, he completely forgot about this matter, but after seeing Hua Lao, Junxin thought of this matter, so by the way, he asked Hua Lao to introduce him on his behalf.

In 1966, Mr. Chen proved Goldbach's conjecture 1+2, and in 1973, he gave an improved version of the 1966 proof in Science China, which shocked the whole world, and was written into textbooks by Britain, the United States, the Soviet Union, France, Japan and other countries, and the results achieved were recognized as "Chen's theorem".

In 1980, he was elected as a member of the Department of Physics and Mathematics of the Chinese Academy of Sciences, and in March 1981, he was elected as a member of the Chinese Academy of Sciences.

When Junxin, Hua Lao and Professor Hu came to the door together, Mr. Chen was waiting for Junxin and the three of them at home because he had received a notice in advance.

Decades later, in the memoirs of the complete works published by Junxin, he described the scene when he first met Mr. Chen Jingrun:

"Mr. Hua informed me in advance that he would bring someone to visit and ask for advice, so on the afternoon of June 20th, I was able to follow Mr. Hu and Mr. Hua to meet Mr. Chen, whose health was not as good as before."

"The first time I met Mr. Chen, I could feel a unique temperament of a mathematician from him, which is indescribable, which is quite imaginary with the temperament of Professor Wiles and Professor Yau Chengtong that I met later."

……

Let's turn our eyes back to the present, Mr. Chen warmly received Junxin and the other three, and after sitting down, Mr. Chen spoke: "I heard that the teacher has come to Beijing a few days ago, and I was planning to take some time to visit you, but I didn't expect you to come to see me!" ”

"There's nothing wrong left and right, I heard Xiaojun say a few days ago that he wanted me to help him introduce you, so come and have a look." Hua Lao waved his hand and pointed out the theme of today's visit.

"Oh, it's Junxin's little brother, right?" Mr. Chen turned to Junxin and said in a kind tone.

"Hello Mr. Chen, don't be surprised to visit!" Jun Xin said as he bowed forward.

"Hehe, little brother Jun don't have to be polite, I have seen your name many times from the newspaper, I have also read the full text of Modell's conjecture in the "Annals of Mathematics", and I have also read Junxin's inference, it can be said that the solution to Fermat's great theorem is right in front of me."

Jun Xin shook his head with a wry smile and said: "Although I have found the key to solving Fermat's theorem, if I want to prove it completely, even if it is at my level, at least I have to give up all other irrelevant work, concentrate all my energy, and spend about seven or eight years to be able to prove it, but this is a bit more than worth the loss for me." ”

Junxin had told Professor Hu this sentence before, but now he just took it out and said it again.

"Is it that difficult?" Hua Lao couldn't help but ask.

Jun Xin said: "The Taniyama-Shimura conjecture involves most of the content of algebraic geometry, what modular form, elliptic lines, etc., and if you want to solve it, it is not just a Moder conjecture that can be compared. ”

"Hehe, isn't that what science is all about? Promote the development of the discipline in solving difficult problems, so as to promote the development of mathematics. Mr. Chen said with a smile.

Junxin shook his head and said, "As early as the opening ceremony of the freshman year of Mizuki University, I mentioned two different people in the scientific world, one is a bird and the other is a frog. At that time, Hua Lao asked me whether I wanted to be a bird or a frog. But I didn't answer, and Hua Lao didn't ask later. After a year of muddled thinking and research, I think maybe I will choose to be a bird and create more things. ”

"Hehe, what a spirit!" Hua Lao approvingly, he was very satisfied with Junxin's choice, there are too many frogs in the scientific community in China, but no one can become a bird, and now there is finally a person with enough ability to stand up and say that he wants to become a bird, Hua Lao is happy from the bottom of his heart.

"Jun Xiao's friendly spirit!" Mr. Chen said with admiration. As for Professor Hu on the side, he is even more in favor of Junxin's approach, in fact, a long time ago, Hujiao has silently paved the way for Junxin to become a bird.

"Don't you know if there's anything you need my help with today?" After the four of them exchanged pleasantries, Mr. Chen took the initiative to ask.

"A few days ago, when I was studying the twin prime conjecture problem, I found that when using the estimation method, I could obtain a sufficient condition and give a proof. At the recommendation of Professor Wang, it has been sent to Acta Mathematica Sinica for publication, and it should be published soon! Then I had a brilliant idea when I was working on the non-estimation method, but this method needs to use the sieve method, and I think that you are the authority on the use of the sieve method in the whole world, so I would like to come and ask you about the sieve method. Junxin sorted out his thoughts and replied seriously.

"Twin prime conjecture problem!" Mr. Chen suddenly laughed and said, "It's a problem of analytic number theory." Part of Hilbert's eighth of 23 questions. There have been some studies in the past to prove Goldbach's conjecture. ”

After a pause, Mr. Chen already understood the part of the question that Junxin wanted to ask, so he took the pen and paper on the table and began to explain his application and research on the Sieve Method in the Goldbach Conjecture, as well as the improvement and innovation of the Sieve Method over the years.

Don't look at the proof of Goldbach's conjecture is only a few short pages, but Mr. Chen spent an hour and a half explaining it, during which there were constant additions from Hua Lao and constant prompts from Professor Hu. Fortunately, it's Junxin, who has a talent for mathematics, and if it were anyone else, it was estimated that even a whole day's work would still be confused about it.

"How did you deal with this ......?"

"If you use this equation and make a ......, the final result is exactly equivalent to the problem, and the above result is obtained."

After asking the last question, Jun Xin breathed a long sigh of relief, he admired Mr. Chen's mathematical attainments very much, especially on the sieve problem, often he asked a question, Mr. Chen did not think about it at all and pointed to the key and core of the problem, after a question and answer, he benefited a lot.

"How? Jun, do you have any questions? Seeing that Mr. Chen's face was a little pale after a lot of thinking, Professor Hu asked out of concern for this senior brother.

Jun Xin shook his head and said, "The questions just now are basically almost all asked, and I also have an understanding of the sieving method." Looks like I'm going to be able to get the problem a little closer. ”

"Oh, tell me?" Hua Lao asked.

"I found a weakened form of the twin prime conjecture in the twin prime conjecture. In my latest research, I found that there are infinitely many prime pairs with a difference of less than 70 million without relying on unproven inferences, and now after this question-and-answer, I estimate that the difference can be narrowed to less than 1,000, which is expected to solve this problem completely. Junxin leaned back, his eyes slightly closed, and replied.