Chapter 158: The Twin Prime Conjecture is a Bit Difficult

Xu Qingzhou was silent, sitting on pins and needles. He finished the orange in a few bites, stood up, and intended to return to the room.

Wang Xiaping said with a smile, "Not eating fruit anymore?"

"I'm going to find my true love," Xu Qingzhou answered expressionlessly. This fruit is not worth eating.

"Little Yao?" Wang Xiaping had a smile on her face, feeling that this kid could be taught, and looked more pleasing to the eye.

Xu Qingzhou waved his hand without looking back, "There is a beauty in the book, I am going to find the beauty."

Bang.

The bedroom door closed.

Dong dong~ Wang Xiaping knocked on the door and came in, put the cut apple on the only empty corner of the table, looked at the sheets of manuscript paper piled on the table, and then looked at the things like ghost charms on the manuscript paper, her heart was complicated.

Read! {

"Prime numbers..." Xu Qingzhou squinted at the paper about twin primes on the screen, his index finger tapping the manuscript paper lightly.

"Chanting spells all day long," Wang Xiaping said with a dark face, "Go buy a bottle of light soy sauce!"

Let a and q be coprime, use π(x; q, a) to represent the number of primes p not exceeding x that satisfy the condition p=a(mod q).

Thinking about it, Xu Qingzhou let out a breath, picked up the manuscript paper, and continued to calculate according to the paper.

Of course, after that, it was Zhang Yitang's paper, which set the difference to 70 million. And one week after the paper was published, Chinese mathematician Tao Zhexuan launched a project to reduce the value as much as possible according to Zhang Yitang's method.

Inside the house, Xu Qingzhou ate a few pieces of apple, heard the nagging sound outside, and couldn't help shaking his head. Old Xu is really something, he can't argue with Wang Nushi, but he just wants to refute a few words every time.

Then to Chen Jingrun, who also proved (1-2) of the Twin Prime Conjecture in his paper proving (1+2) in 1973.

Xu Qingzhou hung up the phone. Just as he turned around, he found Wang Nushi standing at the door.

"You are arguing."

There was no way, he could only slow down, look at some data, and supplement his knowledge.

"Fine, then you tell me where I am arguing."

So far, the fixed value has been reduced from 70 million to 246.

!.

"Rest early, don't stay up late every day."

Wang Xiaping started fantasizing about her retirement life of helping Xu Qingzhou take care of children in the future.

At first, Xu Qingzhou didn't understand the meaning of this sentence. After a week, he finally understood why these scientists were so pessimistic.

Zhang Yitang drew on the sieve method idea of Goldston-Pintz-Yıldırım, but made quite important innovations in prime numbers in arithmetic progressions.

The further you go, twin primes seem to be many, but they become more and more sparse, and there is no pattern. It seems that there are infinitely many groups of twin primes, and this is the Twin Prime Conjecture.

"Mm, okay, that's all. During this period, you will become more familiar with the knowledge of limited compressed light fields. Okay, goodbye."

Bedroom, on the desk, lay sheets of calculation manuscript paper, filled with complex formulas.

Xu Shouyun said, "I think you are just wanting him to give birth to a grandson or granddaughter, so that you can feel at ease." "You don't say, it's really at ease like this. With a home, there is a concern in the heart, so you won't drift around."

"t is the transmittance of the output coupling mirror... When the pulse light pumps the collinear BIBO crystal of type I phase matching (o→e+e), due to the birefringence effect, the spatial walk-off effect will inevitably exist..." Even if it were in the previous life, in the next ten years, Xu Qingzhou didn't hear who solved the Twin Prime Conjecture, although during this period, mathematicians publicly claimed that they proved the conjecture, but it was overturned by others not long after.

Mathematics is based on the establishment of number systems. Integers are very basic, and prime numbers are more basic numbers than integers. The reason why they are important is that any integer greater than 1 can be decomposed into the product of prime numbers.

During this period, he went through the research data of the Twin Prime Conjecture, from the 9-almost prime proved by Norwegian mathematician Brun in 1919, which differ by 2, to 1947, when Hungarian mathematician Rényi proved that there exists a constant k such that there are infinitely many pairs of natural numbers m,

For example, Zhang Yitang proved: for meaningful a, there is ∑|π(x; q; a) - π(x)/φ(q)| < x/(logx)^A. In fact, before the proofs by Zhang Yitang and others, many mathematicians asserted that analytic number theory had reached its end.

"Okay." Xu Qingzhou chuckled. Needless to say, from Wang Nushi's gloomy face, he knew she was likely angry because he hadn't left the house for several days.

"That's true, our son has ambition, we as parents should be happy." Wang Xiaping sighed and said, "But I don't know why, I just don't feel at ease, it's like the feeling of stepping on clouds."

Before Zhang Yitang's paper came out, Chen Jingrun's paper was basically considered the most important proof in analytic number theory in the last 30 years.

Smiling, he picked up his pen and wrote on the draft paper.

"Hoo~"

In the bedroom, he was on the phone with Ren Xiaoling.

There are φ(q) positive integers a that do not exceed q and are coprime to q.

Xu Shouyun couldn't help but say, "A good man has ambitions in all four corners of the world; how can he stay by our side every day? That would make him a parasite."

When a=q=1, π(x; 1,1)=π(x).

In the living room, Wang Xiaping sat down beside Xu Shouyun and said, "Qingzhou is calculating those things again."

During these days, he had used countless sheets of scratch paper, gone through all the formulas in the materials, and then intended to organize his thoughts like before to come up with a plan, but for a moment, he was actually at a loss.

Time flew by, it was 11:30 at night.

The Twin Prime Conjecture has been a parallel conjecture to the Goldbach Conjecture and has always been a key focus of research in the field of number theory.

"Can't one have ambitions in all four corners of the world while staying at home?"

"This brat." Wang Xiaping also realized it at this moment and shook her head helplessly.

Let p be an integer greater than 1. If p has only two factors, 1 and p, then p is called a prime number.

"Alright, I'll go to sleep once I finish this bit."

Although he was at home, Xu Qingzhou's tasks were no fewer than when he was at school. Besides researching the Twin Prime Conjecture, he would look at materials on material physics when relaxing, and occasionally he had to answer questions for Ren Xiaoling far away.

Being able to see the peak of the great mountain that is the Twin Prime Conjecture, but regrettably, there was no path forward. Clearly having treasure in front of him but only being able to look at it—this feeling was very uncomfortable, and it even made one feel a bit desperate.

"You used to chase him around every day, telling him to study. Now that he's studying on his own, you're the one who's not used to it." Xu Shouyun said calmly while drinking tea.

Only Wang Xiaping was at home; old Xu had gone fishing again.

Seeing Xu Qingzhou moving slowly, Wang Xiaping urged, "Alright, hurry up and go buy things. Don't go to the small shop in the residential complex; go to that big supermarket on Wutong Street."

"Fine, I'm going now."

Wang Nushi really went to great lengths to get him to leave the house.

(End of chapter)