The Science Fiction World of Xueba

The reason why Pang Xuelin stopped suddenly was not because he was out of ideas.

In fact, the overall proof of the twin prime number conjecture has already taken shape in his mind, and he just needs to deduce it smoothly.

The reason why he suddenly stopped now is because he found that the proof scheme he used seemed to be able to prove not only the twin prime number conjecture, but also the Polignac conjecture.

The twin prime conjecture states that there are infinitely many prime numbers such that +2 is a prime number.

The Polignac conjecture is an extension of the twin prime conjecture: for all natural numbers k, there are infinitely many pairs of primes (, +2k).

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

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

Pang Xuelin thought for a while, then returned to the fifth blackboard, erased all the derivation process on it, and then wrote it again.

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

"What's wrong with Professor Pang? Is there something wrong with the derivation process just now?"

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

"I think Professor Pang is a bit overbearing. After all, for such a major proposition, the on-site derivation is a bit too hasty."

"It's normal for a young genius to have such a drive, but if you rush too hard, you will easily run into a wall."

"I don't think Professor Pang will be aimless. With his ability, he can prove that the twin prime number conjecture should not be a problem."

...

Pang Xuelin was immersed in his own thoughts, and did not pay any attention to the discussions in the audience.

[Let x be the characteristic of cf, then x=(x), where x is the characteristic of complete f. If π generates a prime ideal of f, then let x()=x(π). In this way, the l function of hacke can be defined by the following formula: l(s, x)=n(1-x()(n)-s)-1]

[Where s is a complex number, with of being the algebraic integer ring of f, then n is the order number of the ring of. It can be proved that: when res\u003e1, l(s, x) is an analytic function, l(s, x) can be extended to a semi-pure function, and there is a function e(s, x), such that l(s, x) Satisfy the equation...]

...

Time passed by every minute and every second.

When Pang Xuelin wrote on the seventh blackboard, Deligne frowned suddenly.

He turned his head and said to Peter Sarneck next to him: "Professor Pang is not proving the twin prime number conjecture, but proving the Polignac conjecture!"

Peter Sarneck nodded thoughtfully and said, "This young man is really surprising!"

Whether it is the twin prime number conjecture or the Polignac conjecture, it is a well-known problem in the history of mathematics.

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

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

For a moment, everyone was excited and shocked.

"Unexpectedly, Professor Pang actually conjectured on Polignac."

"Professor Pang paused just now. Could it be that during the derivation process, he had a sudden inspiration and found a breakthrough in Polignac's conjecture?"

"It's very possible. Professor Pang is becoming more and more unexpected."

"I don't know if Professor Pang can successfully prove it."

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

...

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

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

Three hours passed in a flash.

[Assuming r2|r, then when 0≤k\u003cr2, then we know that ∑{r2,‖r2(+k)q‖-1}\u003c\u003cr2ζ】

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

Pang Xuelin looked at his results of nearly three hours, put down the chalk, shook his slightly sore wrist, walked to the microphone on the reporting platform, and said with a smile: "In 1849, Alfond de Polignac proposed the general Conjecture: For all natural numbers k, there are infinitely many pairs of prime numbers (, + 2k). I think, today, the answer has come out.”

A needle drop could be heard quietly in the auditorium.

Qi Xin was a little worried: "Sister Zhi, junior, does this prove that the result is correct?"

Sophon looked approvingly at the ten blackboards arranged in a semicircle on the stage, and said with a faint smile, "Don't worry, there's nothing wrong with it!"

On the other side, Peter Sarneck looked at Pang Xuelin in disbelief, turned his head to look at Deligne and said, "Professor Pang...is it really proven?"

Deligne nodded and said, "It's proven!"

clap clap...

After all, Deligne stood up first and paid tribute to Pang Xuelin with applause.

Immediately afterwards, applause swept the entire auditorium like a tide.

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

Pang Xuelin smiled and said: "Thank you, everyone. Next is the questioning session. If you have any questions about this proof process, you can ask them at any time."

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

Everyone whispered to each other and talked a lot.

The proof requirements for mathematical conjectures have always been rigorous. Among the people present, no more than one-third of them can really keep up with Pang Xuelin's thinking and understand the entire proof process.

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

So soon it was up to people to raise their hands and ask questions.

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

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

"Professor Pang, I'm Andrew White, a postdoctoral fellow in the Department of Mathematics, New York University. You said in Proposition 2110, how did you determine that x is a closed subset of gb?"

Pang Xuelin said with a slight smile: "For any s ∈ s, define the mapping s: gb→gbxgb, obviously, s is also a morphism as the product of morphisms mapping the cluster gb to itself, and this is an identity morphism, and because The nature of the cluster, we can determine that for the corner element set d is a closed subset of gbxgb, so we can determine that x is a closed subset of gb!"

"Thank you, Professor Pang! I have no problem."

After Andrew White sat down, someone raised his hand to ask a question.

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

After repeatedly confirming that no one asked questions, the host of the report meeting announced the end of the report meeting.

At this time, the news of Pang Xuelin's proof of Polignac's conjecture began to spread rapidly to the mathematical community centered on Princeton.