Chapter 65 You Actually Completed the Proof
Lu Chunming was naturally familiar with Carmichael numbers in number theory, but he also knew that since three overseas mathematicians, including Pomerance, completed the proof of infinite Carmichael numbers nine years ago, the problem of the intervals between them has remained unresolved.

Many mathematicians who study number theory, both at home and abroad, have studied this problem.

Unfortunately, there was no substantial gain in the end.

Therefore, when he saw the title of Xu Yuan's paper, he didn't know whether the other party had advanced the proof of this problem or whether it was a wrong method from the beginning.

If it is the latter, it is a bit regrettable but normal, but if it is the former, it is a big event in the number theory circle.

Putting these thoughts aside for the moment, he focused on the specific content of the paper.

However, as time passed, more and more beads of sweat appeared on Lu Chunming's forehead.

His brows were furrowed.

The whole face seemed to interpret the word "embarrassment".

Although he was reluctant to admit it, the reality was that he simply could not understand the proof process of the paper.

Not to mention whether the argument is correct.

At this point, he finally understood why Xu Yuan was so liked by Professor Tang.

Regardless of whether the methods used in the paper are accurate, at least they are beyond his level in the field of number theory.

Faced with this embarrassing situation, he had no choice but to turn his head and look in the direction of Tang Shihong.

He shouted twice in a low voice.

"tutor."

"Please come over here first."

Upon hearing this, Tang Shihong stopped what he was doing again and glanced at Lu Chunming with some impatience.

"what happened again?"

"I don't understand the paper written by my junior fellow student." Lu Chunming answered truthfully.

But when Tang Shihong heard this, it was a big deal.

The next second he suddenly stood up from his chair and gave Lu Chunming a violent scolding, without giving any face in front of others.

"can't read?"

"I usually ask you to listen carefully to the lectures and train your logical thinking, and go to the school library more often to study literature. See if you still look like a graduate student now."

Tang Shihong knew that Xu Yuan's talent was not comparable to that of ordinary undergraduates, but after all, he had never taken systematic university courses. Logically speaking, even if the content of the thesis was a bit niche, with Lu Chunming's graduate degree, he should not be unable to understand it.

The key point is that Lu Chunming is a graduate student he recruited after all. Now he can't even understand the thesis of undergraduate freshmen. Doesn't it show that his level is very limited?

Although Lu Chunming guessed that he would be criticized, he still couldn't bear it in front of his future junior fellow apprentice.

I could only reply somewhat aggrievedly: "But Junior Brother Xu Yuan's paper is about proving the interval problem between infinite Carmichael numbers."

"What did you say?"

Tang Shihong, who was originally furious, his expression froze instantly when he heard these words.

"Carmichael number problem?"

He repeated something to himself, then suddenly thought of something and walked towards Lu Chunming.

He knew that Xu Yuan was trying to study the Carmichael number problem, but he felt that this problem was not suitable for Xu Yuan, and it would be a complete waste of time to continue to invest too much energy in it.

Without a solid mathematical foundation and strong talent, it would be impossible to fully prove it.

He thought Xu Yuan had given up on this problem long ago, but he didn't expect that he was still studying it.

Even wrote a paper.

As his thoughts raced, a bold guess emerged in his mind uncontrollably.

Is it...

When Lu Chunming saw the professor coming, he finally breathed a sigh of relief and quickly stood up to give up his seat.

Xu Yuan stood by and remained silent the whole time, not saying a word to protect Lu Chunming's self-esteem.

It was normal that Lu Chunming couldn't understand the number theory problem that had not been solved in the mathematics community for nearly a decade, but he didn't expect the other party to explain it directly.

It is really very brave.

At this moment, the only thing Tang Shihong had in his eyes was the paper. He sat down with his eyes fixed on the screen.

He was also surprised when he saw the title of the paper above.

Although he really hoped that this was true, his reason told him that it was too unbelievable.

Suppressing these emotions for the time being, he calmed down and carefully reviewed the mathematical paper.

First of all, the content is standard and there are not many problems with the format. It doesn't look like something that a freshman could have written.

Even the graduation theses submitted by senior students in the department cannot reach the level of Xu Yuan's.

As time passed, Tang Shihong's expression became more and more solemn and serious, as if he was a traveler in the desert who finally found an oasis and absorbed the nutrients in the paper greedily.

I don't know how much time passed before he finally responded.

He stretched out his hand and said a few words lightly: "Draft paper and pen."

As expected of Tang Shihong's graduate student, Lu Chunming immediately took the draft book and pen next to him and handed them over upon hearing the voice.

"To the instructor."

They cooperate with each other very well.

Tang Shihong took the draft paper and pen, pushed the keyboard aside, and quickly verified the formula in the paper. The process made the atmosphere around him a little tense. Lu Chunming dared not to breathe, for fear of disturbing his tutor.

Xu Yuan waited calmly with a calm expression. He could not be more confident in his own proof process.

No matter how you verify it, there is only one result.

Completely correct.

After some time passed, Tang Shihong finally stopped calculating, straightened his back and did not hide the ecstasy on his face at all.

He kept murmuring in his mouth.

"That's right."

“It turned out to be right.”

"It's really ingenious, proving the interval by improving the sieve method."

"This is definitely a major result in number theory."

When Lu Chunming heard these words, his heart was suddenly filled with turmoil and he couldn't help but look at Xu Yuan beside him.

"It can make the mentor react like this."

"Could it be possible that this has really advanced the proof of the gap problem between infinite Carmichael numbers..."

Tang Shihong quickly came to his senses, forced himself to control his inner excitement and slowly turned around.

However, he did not look at Xu Yuan immediately. Instead, he fixed his eyes on Lu Chunming and said in a gentle tone, "The instructor just blamed you wrongly. It is normal that you cannot understand Xu Yuan's paper."

Although Lu Chunming felt something was strange when he heard this, he felt much better when he thought that he would not be criticized.

He immediately stated: "It's because I didn't listen carefully to your teachings, Master."

Unfortunately, before he could really feel happy, Tang Shihong's voice rang in his ears again.

"Then go get Xu Yuan a glass of water first."

"Okay, mentor." Lu Chunming agreed without any hesitation.

Just as he turned around and took two steps towards the water dispenser, he suddenly found that his mentor took the initiative to pull a chair for Xu Yuan and invited Xu Yuan to sit down next to him with a smile on his face.

"Come sit here and talk about your paper slowly."

"Actually, after reading the materials you sent me, Professor Tang, I have been trying to find a way to prove the Carmichael number gap problem." Upon hearing this, Xu Yuan sat down and talked about his proof process: "Until I got inspiration during the International Mathematical Olympiad, and finally completed the proof of the gap problem by improving Mr. Chen Jingrun's weighted sieve method."

"It is concluded that when n>3300, there is always a Carmichael number between n and 2n."

"Because there is no computer in my hometown, I finally finished writing this paper in the school computer room during the free time during military training after school started."

Tang Shihong was already shocked by the proof process in the paper, and now after listening to Xu Yuan's story, he found it even more unbelievable.

He still remembered that after the International Mathematical Olympiad, Hu Zhiwei once mentioned to him that Xu Yuan was the last one to hand in his paper.

I'm afraid the other party would never have thought that Xu Yuan was proving the proof of the Carmichael number interval problem in the examination room.

The key is also ultimately proven success.

This event itself is a miracle.

"You dare to prove a difficult math problem in an exam. I'm afraid there's no one else like you in all the International Mathematical Olympiads."

"You have given me another huge surprise, which has taken the entire field of number theory by surprise."

"Do you know Xu Yuan?"

"Once your paper is published, it will cause a sensation in the mathematics community."

"Carmichael numbers are closely related to the security of cryptographic communications, and your proof method may also be applicable to smaller intervals."

“Who would have thought that a difficult problem in number theory that had remained unsolved for nine years would be completely proven by a newly enrolled undergraduate student?”

Lu Chunming, who was walking over with a cup in his hand, was stunned when he heard his mentor's last words.

In his understanding, Xu Yuan's ability to advance the proof showed that he was a rare mathematical genius. He never expected that he would actually directly complete the last proof of Carmichael numbers.

Almost subconsciously, he blurted out, "Brother, did you really solve the last problem of the Carmichael number?"

"His math talent is much better than yours. If nothing unexpected happens, Xu Yuan will definitely achieve more than me in the future." Tang Shihong rolled his eyes at Lu Chunming mercilessly, and then hurriedly urged: "Hurry up and bring the water over."

"Okay, mentor."

After Lu Chunming figured out the situation, he not only did not take his tutor's double standard attitude to heart, but became more attentive to Xu Yuan.

If you don't build relationships with this future math giant now, when will you?

"Brother, drink some water. Do you want some snacks?"

"No need to trouble you, senior brother." Xu Yuan was also startled and waved his hands quickly.

In the following time, Tang Shihong brought the topic back on track. After a little thought, he said, "I was also surprised by your talent in the paper. Except for a few formatting issues, there is no need to revise it at all."

"I'll work overtime today to get it for you. Come pick it up from me tomorrow."

"Then I'll trouble you, Professor Tang." Xu Yuan nodded to express his gratitude.

After finishing the thesis, he realized that it was almost midnight. Unable to resist Lu Chunming's enthusiastic attitude, they had to go to the school cafeteria to eat together and let the other party pay for it.

As for Tang Shihong, he obviously had no interest in other things and said he wanted to work overtime to revise the format of the paper.

I only gave Lu Chunming some money to help bring some food.

At the same time, in the boys' dormitory of Zijing Apartment, Li Zhenya, Wang Haitao, Liu Yang and the others were discussing Xu Yuan, and they all speculated what Xu Yuan had done and why he had not returned yet.

(End of this chapter)