If these words were just uttered by an eighteen-year-old boy who didn't know a single one, then neither Professor Wang nor Professor Qiao would take it seriously, at most they would only think that this was a little guy with a heart higher than the sky and didn't know what to say. But in this case, from Junxin, who solved the world-class problem of Modell's conjecture at the age of seventeen, Professor Wang and Professor Qiao couldn't help but choose to believe it, or at least seemed to be skeptical.

"It's going to be a long time," Professor Wang lamented.

Jun Xin laughed: "I estimate that it will take at least thirty years, at least two generations of people to work together!" But what I don't lack is time, after all, sometimes youth is a hard injury, but sometimes youth is also a cost. ”

"Is that why you work as a researcher at the Mizuki Institute of Mathematics and don't participate in applied research?" Professor Qiao asked.

"Yes and no!" Junxin explained, "It's because I'm just a freshman now, after all, I haven't grown up yet, and the professors deliberately did this to protect me and assigned me directly to theoretical research. Although applied mathematical research can produce results quickly and produce results quickly if you find the direction, it is easy to limit researchers to one field, and I don't want to be confined to a certain field and miss out on some wonderful ideas. ”

"Your heart is indeed very big, but you should also understand the current situation, and you will not have any scruples?" Professor Qiao said cryptically.

Professor Qiao's meaning Junxin naturally understands that after the end of the ten years of ****, no one knows if it will happen again, or whether some things can be solved in a short period of time, no one knows. Therefore, he implicitly persuaded Junxin to act more steadily.

"Elder Qiao, I naturally know your opinion, but there is a reason why I did this." Jun Xin shook his head and said, "The most creative age of mathematicians is generally between 20 and 35 years old, and the study of mathematics is actually more about inspiration, and ninety-nine percent of the sweat in the study of mathematics is useless, only the one percent of inspiration is the most important." ”

"Now I have a strong interest in many problems in mathematics, and recently when I was writing the content of the related subject branch of the foundation of algebraic geometry, I became interested in some very interesting contents, and I have done some research on some of these problems, and have achieved some results. I think that these problems and results can be summed up in my own mathematical system. ”

"Oh, what's the problem?"

Jun Xin shook his head and said, "Recently, when I was studying the connection between number theory and algebraic geometry, I became somewhat interested in the eighth of Hilbert's twenty-three problems. ”

"Is it a problem with prime numbers?" Professor Qiao said with a little surprise, "The Riemann conjecture, the Goldbach conjecture and the twin prime conjecture?" Do you have any new ideas? ”

"It's a matter of twin prime conjectures." Junxin smiled and said.

A twin prime is a pair of prime numbers that differ by 2, such as 3 and 5, 5 and 7, 11 and 13, etc. This conjecture was formally formulated by Hilbert in the report of the International Congress of Mathematicians in 1900, question 8, and can be described as follows:

There are infinitely many primes p, such that p+2 is prime, and the pair of primes (p,p+2) is called twin primes. In 1849, Alfon de Polliniac proposed a general conjecture that there are infinitely many pairs of prime numbers (p, p+2k) for all natural numbers k. The case of k = 1 is the twin prime conjecture. When k is equal to other natural numbers, it is called the weak twin prime conjecture (i.e., a weakened version of the twin prime conjecture). Therefore, some people have put Polygnac as the proposer of the twin prime conjecture.

In 1921, British mathematicians Godfrey Hardy and John Littlewood proposed a conjecture similar to the Polliniac conjecture, commonly known as the "Hardy-Littlewood conjecture" or the "strong twin prime conjecture" (i.e., an enhanced version of the twin prime conjecture). This conjecture not only proposes that there are infinitely many pairs of twin primes, but also gives their asymptotic distribution.

The latest proof of the twin prime conjecture was made by the Chinese mathematician Mr. Zhang Yitang. He proved a weakened form of the twin prime conjecture. In his latest study, Zhang Yitang discovered the existence of infinitely many pairs of prime numbers with a difference of less than 70 million without relying on unproven inferences, thus taking a big step forward on the important problem of twin prime conjecture.

Zhang Yitang's paper was published on the Internet on May 14 and officially published on May 21. On May 28, this constant dropped to 60 million. Just two days later, on May 31, it dropped to 42 million. Three days later, on June 2, it was 13 million. The next day, 5 million. June 5, 400,000.

In the "Polymath" project initiated by British mathematician Tim Gowers and others, the twin prime problem has become a model of cooperation among mathematicians around the world using networks. The continuous improvement of Zhang Yitang's proof has further narrowed the distance between the final solution of the twin prime conjecture. In February 2014, Zhang Yitang's 70 million had been reduced to 246.

"Where have we been?" Professor Wang asked excitedly. In that year, when Mr. Chen Jingrun proved Goldbach's conjecture 1+2, he was the one who reviewed the manuscript, which was a major breakthrough point for Chinese people to be strong in mathematics. And now, in the same field of prime number research, a new mathematical conjecture is about to make a major breakthrough, and he can't help but be excited.

"I just have some ideas, and I still lack some methods!" Junxin frowned and said, "I still use the sieve method, and there are still some questions that have not been clarified in this research, so I want to take a time to communicate with Mr. Chen Jingrun and deepen my knowledge in this area." ”

"Oh!" Professor Wang was a little disappointed with Junxin's answer, but nodded in agreement. Mathematics has always been like this, the pursuit of extreme perfection. The slightest flaw can ruin a proof. Just like when Professor Wiles proved Fermat's theorem again, it was because of a small loophole that his results were almost ruined. Later, if it weren't for the timely remedy, he might have given up proving this conjecture that challenged the limits of human thinking.

"When are you going to leave?"

"Go?"

"Go find Jingrun!"

"Oh, I'm not sure yet." Jun Xin touched the back of his head and said, "After all, prime numbers are not the main direction of my current research, I just have such an idea, in fact, even if I don't have to communicate with Mr. Chen, I can prove that after all, I can see his paper, and I can naturally learn from his method." ”

"And when will your thesis be finished?"

"After meeting Mr. Chen."

"When are you leaving?"

"Didn't you say that?" Junxin was a little unimpressed by the excitement of the two professors.

"Either write your essay or go!" Professor Wang said categorically, and Professor Qiao on the side couldn't stop nodding in approval.

I...... Junxin wants to cry without tears, two stubborn professors.