The reason why Pang Xuelin suddenly stopped was not without ideas.

In fact, the overall proof idea of the twin prime conjecture was already taking shape in his mind, and he only needed to deduce it smoothly.

The reason why he stopped abruptly now was that he found that the proof scheme he was using did not seem to prove not only the twin prime conjecture, but also the Polliniac conjecture.

The twin prime conjecture refers to the existence of an infinite number of primes p, such that p+2 is prime.

The Polignac conjecture, on the other hand, is a generalized form of the twin prime conjecture: for all natural numbers k, there are infinitely many pairs of prime numbers (p, p+2k).

When k = 1, the Polliniac conjecture is equivalent to the twin prime conjecture.

As long as the Polygnac conjecture is proved, then the twin prime conjecture is naturally self-evident.

Pang Xuelin thought about it, went back to the fifth blackboard, erased all the derivation process on it, and then rewrote it.

For a while, there was a lot of discussion in the audience.

"Professor Pang, what's wrong? Could it be that there is something wrong with the derivation process just now? ”

"I don't know, maybe Professor Pang has a new idea."

"I don't think Professor Pang is a little overbearing, after all, for such a major proposition, on-site derivation is really too hasty."

"It's normal for a young genius to have such momentum, but if you rush too hard, it's easy to hit a wall."

"I don't think Professor Pang will be untargeted, and with his ability, he will prove that the twin prime conjecture should not be a problem."

……

Pang Xuelin was immersed in his own thoughts, and he didn't care about the discussion in the audience.

[Let x be the characteristic of Cf, then x=(Xp), where Xp is the characteristic of complete Fp.] If the element π to generate Fp is ideal, then let X(p)=Xp(π). Thus, Hacke's L function can be defined by the following formula: L(s,X)=∏(1-X(p)(Np)^-s)^-1】

[where s is a complex number, and OF is denoted as an algebraic integer ring of F, then Np refers to the order of the ring OF/P.] It can be proved that when Res>1, L(s,X) is an analytic function, L(s,X) can be extended to a semipure function, and there is a function ε(s,X) such that L(s,X) satisfies the equation ......]

……

Minutes and seconds passed.

When Pang Xuelin wrote the seventh blackboard, Deligne's brows suddenly wrinkled.

He turned his head and said to Peter Sanek beside him, "Professor Pang is not proving the twin prime conjecture, but the Polygnac conjecture!" ”

Peter Sanek nodded thoughtfully and said, "This young man is really amazing! ”

Both the twin prime conjecture and the Polygnac conjecture are well-known puzzles in the history of mathematics.

No one expected that Pang Xuelin would challenge this problem at this moment.

In fact, at this time, not only Peter Sanek but also Pierre Deligne, other well-known scholars in the lecture hall also saw Pang Xuelin's ideas one after another.

For a while, everyone was excited and shocked.

"Unexpectedly, Professor Pang actually attacked the Polygnac conjecture."

"Professor Pang paused just now, could it be that in the process of derivation, he had a sudden inspiration and found a breakthrough in Polygnac's conjecture?"

"Chances are, Professor Pang is getting more and more unexpected."

"I don't know if Professor Pang can succeed in proving it."

"I hope so, at least for now, I don't see too many problems in the previous proof process."

……

In the following time, the discussion in the audience did not stop.

Many people even took out pen and paper on the spot to verify Pang Xuelin's proof process.

Three hours was a flash.

[Suppose r2|r, then there is r2/q=-q/r2+1/qr2(mod 1), and when 0≤k

[To sum up: for all natural numbers k, there are infinitely many pairs of prime numbers (p,p+2k)]

Pang Xuelin looked at the results of his nearly three hours, put down the chalk, shook his slightly sore wrist, walked to the microphone of the lecture desk, and said with a smile: "In 1849, Alfon de Polliniac put forward a general conjecture: for all natural numbers k, there are infinitely many pairs of prime numbers (p, p + 2k). I think, today, the answer is out. ”

The auditorium was quietly pin dropping.

Qi Xin was a little worried: "Sister Zhi, junior brother, is this proof that the result is correct?" ”

Tomoko looked approvingly at the ten blackboards on the stage that were arranged in a semicircle, and said with a faint smile: "Don't worry, there's no problem!" ”

On the other side, Peter Sanek looked at Pang Xuelin with some incredulity, turned his head to look at Deligne, and said, "Professor Pang...... Did it really come out? ”

Deligne nodded and said, "It's out!" ”

Bang Bang Bang ......

After that, Deligne took the lead in getting up and paid tribute to Pang Xuelin with applause.

Immediately afterward, applause swept through the auditorium like a tide.

It wasn't until a few minutes later that the applause gradually stopped.

Pang Xuelin smiled: "Thank you, the next step is the question session, about this proof process, if you have any questions, you can ask questions at any time." ”

As soon as these words came out, the audience was in a commotion.

One by one, everyone exchanged ears and discussed.

The proof requirements of mathematical conjecture have always been rigorous, and among the people present, no more than one-third of the people present can really keep up with Pang Xuelin's train of thought and understand the entire proof process.

But even these people who understand it dare not guarantee that Pang Xuelin's proof process is foolproof.

Therefore, it was not long before someone raised their hand to ask questions.

The on-site staff handed the microphone to the other party.

The question was asked by a tall, thin, bespectacled young scholar who looked to be in his early thirties.

"Professor Pang, I'm Andrew White, a postdoc in the Department of Mathematics at New York University, and you said in proposition 2.1.10, how did you determine that X is a closed subset of G/B?"

Pang Xuelin smiled slightly and said: "For any s∈S, define the mapping s: G/B→G/B× G/B, obviously s as the product of the morphism of the mapping cluster G/B to itself, it is also a morphism, and this is an identity morphism, and due to the nature of the cluster, we can determine that for the closed subset of G/B × G/B, we can determine that X is the closed subset of G/B!" ”

"Thank you, Professor Pang! I don't have any more problems. ”

As soon as Andrew White sat down, someone raised his hand to ask another question.

Next, Pang Xuelin took nearly an hour to answer most of the questions.

After making sure that no one asked questions, the presiding officer of the report meeting announced the end of the report meeting.

At this time, the news that Pang Xuelin proved Polignac's conjecture began to spread rapidly to the mathematical community with Princeton as the center.

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