Chapter 158 The twin prime conjecture is a bit difficult
Xu Qingzhou was silent, as if he was sitting on pins and needles. He finished the orange in three times, got up, and planned to go back to the house.
Wang Xiaping said with a smile: "You don't want to eat fruit anymore?"
"I want to find my true love." Xu Qingzhou replied expressionlessly, it doesn't matter if he doesn't eat the fruit.
"Xiao Yao?" Wang Xiaping had a smile on her face. She felt that this kid was teachable and she looked much more pleasing to the eye.
Xu Qingzhou waved his hands without looking back, "There is Yan Ruyu in the book. I want to find Yan Ruyu."
Bang.
The bedroom door closes.
"This brat." Wang Xiaping also reacted at this time and shook her head helplessly.
In the bedroom, on the desk, there are sheets of calculation paper spread out, filled with complex formulas.
"Prime numbers." Xu Qingzhou squinted at the paper on twin prime numbers on the screen and tapped the paper with his index finger.
Suppose p is an integer greater than 1. If p has only two factors, 1 and p, then p is called a prime number.
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.
The further you go, the twin prime numbers seem to be numerous, but you can find that they are becoming more and more sparse and irregular. There seem to be infinite groups of twin prime numbers, and this is the twin prime number conjecture.
The twin prime conjecture is regarded as a parallel conjecture to Goldbach's conjecture and has always been the focus of research in the field of number theory.
During this period, he reviewed the research data on the twin prime conjecture. From 1919, Norwegian mathematician Brun proved that there are infinite pairs of 9-almost prime numbers, and the difference between them is only 2, to 1947, Hungarian mathematician Reni , proves that there is a constant k such that there are infinite pairs of natural numbers m and p.
Turning to Chen Jingrun, in his 1973 paper proving (1+2), he also proved the twin prime conjecture (1-2).
Before Zhang Yitang's paper came out, Chen Jingrun's paper was basically considered the most important argument in analytic number theory in the past 30 years.
Of course, after this, came Zhang Yitang's paper, which set the difference to 70 million. A week after the paper was published, Chinese mathematician Tao Zhexuan launched another project to reduce the value as much as possible according to Zhang Yitang's method.
So far, the fixed value has been reduced from 70 million to 246.
Even in his previous life, Xu Qingzhou had not heard of anyone solving the twin prime conjecture in the following ten years. Although some mathematicians seemed to have publicly claimed to have proved the conjecture, it did not take long for them to be overturned.
"Huh~"
Thinking about it, Xu Qingzhou let out a breath, picked up the manuscript paper, and continued to make calculations based on the paper.
Time flies by, it’s 11:30 in the evening.
Dong Dong~
Wang Xiaping knocked on the door and came in. She put the cut apples on the corner of the only empty table. She looked at the piles of manuscript papers on the table and then looked at the things on the manuscript papers that looked like ghost drawings. She felt in her heart That's complicated.
"Go to bed early and don't stay up late every day."
"Okay, let's go to bed after finishing this."
In the living room, Wang Xiaping sat down next to Xu Shouyun and said, "Qingzhou is calculating those things again."
"You used to chase him behind him every day and let him study. Now that he has studied on his own, you are not used to it." Xu Shouyun drank tea and said calmly.
"Yes, our son is motivated, and we parents should be happy." Wang Xiaping sighed and said, "I don't know why, but I just feel uneasy, like I'm stepping on a cloud."
Xu Shouyun said: "I think you just want him to give birth to grandchildren, so that he can feel at ease." "Don't tell me, this will really make you feel at ease. If you have a family, you will have care in your heart, so you won't Floating around.”
Wang Xiaping began to fantasize about her retirement life of helping Xu Qingzhou take care of her children again.
Xu Shouyun couldn't help but say: "A good man has his ambitions in all directions. How can he stay by our side every day? He won't be gnawing at the old man."
"Can't you just focus on the whole family and focus on all directions?"
"You are making excuses."
"Okay, then you can tell me where I made the argument."
Inside the house, Xu Qingzhou ate a few pieces of apples. Hearing the chatter outside the house, he couldn't help but shake his head. Lao Xu really couldn't say anything to Ms. Wang, but he just wanted to refute a few words every time.
Smiling, he picked up his pen and wrote on the manuscript paper.
Assume that a and q are relatively prime, and use π(x;q,a) to represent the number of prime numbers p that satisfy the condition p=a(modq) not exceeding x.
When a=q=1, π(x;1,1)=π(x).
There are φ(q) positive integers a that do not exceed q and are relatively prime to q.
Zhang Yitang drew on the sieve method idea of Goodstone-Pintz-Yildirim, but made important innovations in the use of prime numbers in arithmetic progressions.
For example, Zhang Yitang proved that: for meaningful .a, there is ∑|π(x;q;a)-π(x)\φ(q)|x\(logx)^
In fact, in Zhang Yitang et al. Before the human proof, many mathematicians asserted that analytic mathematics has come to an end.
At first, Xu Qingzhou didn't know what this meant. After a week, he finally understood why these scientists were so pessimistic.
During these days, he used countless calculation papers and went through the calculations in all the materials. He then planned to organize his thoughts and come up with a plan as before, but for a while he was at a loss.
Only when you can see the twin prime numbers can you guess the peak of this mountain. Unfortunately, there is no road ahead. There is clearly a treasure in front of you, but you can only look at it. This feeling is very uncomfortable and can even make people feel a little desperate. .
He had no choice but to take it slow first, and then read some information to supplement his knowledge.
Although he was at home, Xu Qingzhou had no less things to do than at school. In addition to studying the twin prime number conjecture, he also read information on material physics when he relaxed, and occasionally had to answer questions for Ren Xiaoling who was far away.
In the bedroom, he was calling Ren Xiaoling.
"T is the transmittance of the output coupling mirror. When pulsed light pumps a type I phase-matched (o→e+e) collinear BIBO crystal, there will inevitably be a spatial walk-off effect due to the birefringence effect."
"Well, okay, that's all. During this time, you can become more proficient in limiting compressed light fields. Goodbye."
Xu Qingzhou hung up the phone and as soon as he turned around, he found Ms. Wang standing at the door.
"One day is like reciting a mantra." Wang Xiaping said with a sullen face, "Go buy a bottle of light soy sauce!"
"Okay." Xu Qingzhou chuckled. Needless to say, from Ms. Wang's gloomy face, she knew that she was probably angry because she hadn't been out for several days.
Wang Xiaping was the only one at home, and Lao Xu went fishing again.
Seeing Xu Qingzhou taking his time, Wang Xiaping urged, "Okay, hurry up and buy something. If you don't want to go to the small store in the community, go to the big supermarket on Wutong Street."
"Okay, go now."
Ms. Wang also took great pains to get herself out of the house.
(End of chapter)