Chapter 158 The Twin Prime Conjecture is a bit difficult Xu Qingzhou was silent, feeling very uncomfortable. He finished the orange in a few bites, stood up and prepared to go back to the house. Wang Xiaping smiled and said, "Don't you want to eat fruit?" "I want to find my true love." Xu Qingzhou answered expressionlessly. It would be better not to eat the fruit. "Xiao Yao?" Wang Xiaping had a smile on her face. She felt that this boy was teachable and looked much more pleasing to the eye. Xu Qingzhou waved his hand without looking back, "Yan Ruyu is in the book. I want to go find Yan Ruyu." boom. The bedroom door closed. "This brat." Wang Xiaping also reacted at this time and shook her head helplessly. In the bedroom, on the desk, there were sheets of calculation paper filled with complicated formulas.
"Prime numbers?" Xu Qingzhou squinted at the paper on twin prime numbers on the screen, tapping the manuscript lightly 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. Integers are very basic when it comes to establishing the number system in mathematics, and prime numbers are even more basic than integers. The reason why they are important is that any integer greater than 1 can be decomposed into the product of prime numbers. As we go further in time, the number of twin primes seems to be large, but we can find that they are becoming increasingly sparse and irregular, as if there are infinite sets of twin primes, and this is the twin prime conjecture. The twin prime conjecture is regarded as a parallel conjecture to the Goldbach conjecture and has always been a focus of research in the field of number theory. During this period, he reviewed the research materials on the twin prime conjecture, from the proof by Norwegian mathematician Brun in 1919 that there are infinite pairs of 9-near prime numbers, with a difference of only 2 between them, to the proof by Hungarian mathematician Reni in 1947 that there exists a constant k such that there are infinite pairs of natural numbers m and p. 再到陈景润，其在1973年证明（1+2）的论文中，其实也证明了孪生素数猜想的（1-2）。 Before Zhang Yitang's paper came out, Chen Jingrun's paper was basically considered to be the most important argument in analytic number theory in the past 30 years. Of course, after that, Zhang Yitang's paper put the difference at 7000 million. And a week after the paper was published, Chinese mathematician Terence Tao launched another project to reduce the value as much as possible based on Zhang Yitang's method. So far, the fixed value of 7000 million has been reduced to 246. Even in his previous life, in the next ten years, Xu Qingzhou had not heard of anyone solving the twin prime conjecture. Although it seemed that a mathematician publicly claimed that he had proved the conjecture, it was soon overturned. "Whoo~" After thinking for a while, Xu Qingzhou let out a breath, picked up the manuscript paper, and continued to make calculations based on the paper. Time flies, it's 11: at night. dong dong~ Wang Xiaping knocked on the door and came in. She put the cut apples on the only empty corner of the 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 paintings. She felt complicated. "Go to bed early and don't stay up late every day." "Okay, let's go to bed after this." In the living room, Wang Xiaping sat down next to Xu Shouyun and said, "Qingzhou is calculating those things again." "Didn't you always chase after him and ask him to study? Now he goes to study on his own, and you are not used to it." Xu Shouyun said calmly while drinking tea.
"Yes, my son is ambitious, and we as parents should be happy." Wang Xiaping sighed and said, "But I don't know why, I just feel uneasy, like I'm walking on clouds." Xu Shouyun said, "I see that you just want him to give you grandchildren, so that you can feel at ease." "You know what, this really makes you feel at ease. Having a home will give you something to worry about, and you won't be wandering around." Wang Xiaping began to fantasize about her retirement life when she would help Xu Qingzhou take care of the children. Xu Shouyun couldn't help but say, "A good man should have ambitions to go far and wide. How can he stay with us every day? That would make him a parasite." "If you stay at home, can't you have ambitions to go far?" "You are just being argumentative." "Okay, then tell me where I am being rude." Inside the house, Xu Qingzhou ate a few pieces of apple. Hearing the nagging voice outside the house, he couldn't help shaking his head. Old Xu was really something. He couldn't argue with Ms. Wang, but he just wanted to refute her every time. Smiling, he picked up the 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 not exceeding x that satisfy the condition p=a(modq). When a=q=1, π(x;1)=π(x). There are φ(q) positive integers a that do not exceed q and are relatively prime to q. Zhang Yitang borrowed the sieve method idea from Goodstone-Pints-Yildirim, but made quite important innovations in the arithmetic series of prime numbers. For example, Zhang Yitang proved that for a meaningful .a, there is ∑|π(x; q; a)-π(x )\φ(q)|x\(log x)^ In fact, before the proof by Zhang Yitang and others, many mathematicians asserted that analytic mathematics had reached its end. At first Xu Qingzhou didn't understand the meaning of this sentence. After a week, he finally understood why these scientists were so pessimistic. During this period of time, he used countless calculation papers and went through all the formulas in the materials. Then he planned to organize his thoughts and come up with a plan as he did before, but for a moment he was at a loss. Only when you can see the twin primes can you guess the peak of this mountain. Unfortunately, there is no road ahead. There is a treasure in front of you, but you can only look at it. This feeling is very uncomfortable and even makes people feel a little desperate. There was no other way, he could only take it slow and read some materials to supplement his knowledge. Although at home, Xu Qingzhou has no less things to do than at school. In addition to studying the twin prime conjecture, he also reads information on material physics when relaxing, and occasionally has to answer questions for Ren Xiaoling who is far away. In the bedroom, he was calling Ren Xiaoling. “T is the transmittance of the output coupling mirror. When pulsed light pumps the type I phase-matched (o→ e + e) collinear BIBO crystal, a spatial walk-off effect is inevitable due to the birefringence effect.” "Well, that's all. During this time, you should master the knowledge of limiting and compressing light fields. Goodbye." Xu Qingzhou hung up the phone and just turned around, he found Ms. Wang standing at the door. "It's like chanting a mantra all day." Wang Xiaping said gloomily, "Go buy a bottle of soy sauce!" "Okay." Xu Qingzhou smiled. Needless to say, from Ms. Wang's gloomy face, he knew that she was probably angry because he hadn't gone out for several days. Wang Xiaping was the only one at home, and Lao Xu went fishing again. Seeing Xu Qingzhou's slow pace, Wang Xiaping urged him, "Okay, go buy something quickly. Don't go to the neighborhood store. Go to the big supermarket on Wutong Street." "Okay, let's go now."
Ms. Wang took great pains to get herself out. (End of this chapter)