Chapter 94: Jianxing
Although the actual meeting was still a month away, Wu Tong only had ten days to prepare the report, so time was still quite tight.
She was about to break her promise as soon as she got home. She apologized to her family and Wu Tong touched her laptop to start browsing information. She didn't go to the study room on purpose, but stayed next to her family. She could see her family members when she looked up, and they could see her at any time when they came in and out.
She can concentrate on her studies without any distractions. She doesn't have high requirements for the external environment. Even if it is noisy and chaotic, it doesn't matter, let alone a relatively quiet home.
Now that you have set a goal, you must achieve it. Don’t just talk big, you must do what you say!
Polignac's conjecture: for all natural numbers K, there are infinite pairs of prime numbers (p, p+2k), where k is a positive integer... The special state of K=1 is the twin prime conjecture. How to extend this form to infinite natural numbers?
Proving this conjecture can put an end to part of Hibbert's eighth question. This premise is based on the four words "proven".
Continuing along the line of thought from Wu Tong's previous twin prime conjecture, Wu Tong wanted to first try to prove the bridge created by the twin primes, and then extend and improve it. Could he create a tool that could crack the Polignac conjecture?
If you want to do your work well, you must first sharpen your tools. If you create good tools, solving problems will be a natural result.
In the field of prime numbers, Wu Tong has countless knowledge reserves, including information available on the market and various bizarre innovative thinking and opinions on arxiv.
Wu Tong has studied too many papers and books on this subject, but he is still a long way from creating a real dragon-slaying sword. Scattered pearls, without a string to string them together, will never become a world-stunning pearl necklace.
Where is the specific way out?
A storm of mathematics once again arose in Wu Tong's mind. She looked up information and continued to deduce. The pen in her hand was an extension of her thinking. She calculated and deduced on the draft paper, eliminating one by one to determine the factors she needed.
The general direction of creating tools is correct. The bridge she built was able to successfully prove the twin prime conjecture, and the direction is indeed consistent.
However, it is not enough to generalize the form of K=I to the infinite natural theory with just this bridge. It is necessary to add new content to it and transform it into a Tai Chi Bridge that can suppress the four directions and communicate the yin and yang in the void. This is her way home.
After three days of continuous multi-directional deduction, Wu Tong set her sights on group theory. The proof of the infinity of prime numbers by Mr. Hibbert, which she had read before, jumped out of her mind and gave her hope for the final proof.
Suddenly, the complicated and confusing ball of yarn had a clear beginning and an end, and began to become simple and clear. Wu Tong smiled softly. He wrote down clear formulas line by line with his pen.
Given...
C(g):GG，Xgxg
·····
Thoughts flowed like a spring, sparks of inspiration continued to emerge, and a spark ignited a prairie fire, and a brand-new proof tool was born. Based on the principle of topological infinite extension, the sieve method was introduced to supplement it, and the group theory method was used to study the problem of the infinity of prime numbers as a whole.
Wu Tong calls it the infinite group proof method. Various mathematical symbols and numbers are connected in her writing to create a mysterious and smooth path to the right path.
She spent half a day sorting out the core content and specific steps of the infinite group proof method.
With perfect tools and everything ready, Wu Tong applied this to her goal this time, the Polignac conjecture.
The problem that was originally separated by a thick veil was finally unveiled, revealing its true face that had been hidden for many years.
···a·c≡b·c(mod m) yields ac–bc≡0(mod m) yields (ab)·c≡0(mod m).
···(m, c)=1, that is, m and c are relatively prime, c can be canceled, a–b≡0(mod m), so a≡b(mod m)···
········
The proposition that for all natural numbers K, there are infinitely many prime pairs (p, p+2k) is proved to be true.
When the last word "established" was uttered, it seemed as if heavenly music had fallen to the earth. In this world, another conjecture and problem that has troubled mankind was transformed into a rule and theorem.
She successfully extended K to the case where K is an infinite natural number!
After stretching his slightly stiff fingers, Wu Tong leaned back and relaxed, closing his eyes and letting out a sigh of relief. In the end, he had not boasted and had accomplished the small goal of conquering Polignac's conjecture!
In the sea of consciousness, the enlightenment stele emitted a bright and radiant light that expanded, nourishing Wu Tong's almost dry and tired brain like a sweet rain from heaven, making up for the consumption of Wu Tong's brain running at high speed in the past two days.
The light surrounding it has become more intense once again. From its initial state of being as thin as a veil and almost invisible, after Wu Tong's continuous learning and acquisition of knowledge, as well as several near-sudden advances in knowledge, he has verified major conjectures and difficult problems, and gained the nourishment of the power of knowledge. It has now become a rich color almost like cow's milk, representing the gradual recovery of the power of the Enlightenment Stele.
A shallow enlightenment flowed through his heart, and the Enlightenment Stone Tablet regained an ability, absolute deduction.
Anything that Wu Tong sees can assist Wu Tong in conducting in-depth analysis and deduction of its nature. Of course, this ability has only been restored to a superficial level at present, and can only deduce and simulate some data, and it must be based on Wu Tong's knowledge system reserves.
However, for Wu Tong, it was a surprise. Absolute direction determination and absolute deduction seemed to be a perfect match.
After a short break, Wu Tong started a new round of work. The proof was made, but it was still just a manuscript, and she still had to organize it into a complete report.
However, this did not take much effort. I spent one day, and in the early morning of the tenth day, which was Wu Tong’s actual birthday, July 29, I finished organizing the report and the first draft of the paper, and uploaded them directly to the website provided by ICM.
It was another night of moonset and sunrise. After a deep rest and some morning exercises, Wu Tong went downstairs to enjoy the sumptuous breakfast prepared by his family.
The fried golden dough sticks are plump and chewy, the refreshing pickles are cut in half, the egg yolks are sizzling with red oil, and the homemade salted duck eggs are my grandma's specialty.
A palm-sized crispy pancake, sandwiched with layers of thinly sliced braised beef and rice oil-cooked eight-treasure porridge. Just looking at it makes people happy, and eating it is even more delicious.
Wu Tong smiled and gave her grandma and aunt a thumbs up. She had been doing in-depth research almost day and night these days, and her family had worked hard to accommodate and take care of her.
"Tongtong has finished the research report!" Xu Meifeng couldn't help but ask cheerfully when she saw Wu Tong's cheerful expression, which was very different from the serious thinking he had in the past few days.
"It's done. There's nothing left to do. Just wait and go there next month to make a report!" Wu Tong nodded in confirmation.
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