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 the moment she got home, and apologized to her family. Wu Tong grabbed her laptop and began browsing. She didn't go to the study specifically, but stayed right next to her family. She could see them when she looked up, and they could see her whenever they came in or 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. You can't just talk big, you must do what you say!
Polignac's conjecture states that for all natural numbers K, there exist 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 can this form be extended to infinite natural numbers?
Proving this conjecture would put a final touch on part of Hibbert's eighth question. This premise is based on the phrase "proven."
Continuing with Wu Tong's previous thinking on the 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 job well, you must first sharpen your tools. If you create good tools, solving problems will come naturally.
In the field of prime numbers, Wu Tong has countless knowledge reserves, including information available on the market and various bizarre innovative thinking and discussions on arxiv.
Wu Tong has studied too many papers and books on this subject, but he is still a long way from forging 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 mathematical storm once again arose in Wu Tong's mind. She searched for 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, relying solely on this bridge is not enough to extend the K=I form to the infinite natural theory. 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 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 brainstorm and gave her a glimmer of hope towards the final proof.
Suddenly, the complicated and confusing ball of yarn had a clear beginning and end, and began to become simple and clear. Wu Tong smiled softly. His pen wrote down clear formulas in a flowing manner.
Given...
C(g):G?G，X?gxg
·····
Ideas flowed like a spring, sparks of inspiration emerged, and a spark ignited a prairie fire, and a brand-new proof tool was born. Based on the principle of infinite topological extension, supplemented by the sieve method, and using group theory methods, this paper comprehensively studies and generalizes the problem of the infinity of prime numbers.
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 substituted this into her goal this time, the Polignac conjecture.
The problem that was originally separated by a thick veil was finally unveiled, revealing the true face of Mount Lu 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 means m and c are relatively prime, c can be canceled, a–b≡0(mod m) and we get 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 descended to the world. In this mortal world, another conjecture and problem that has troubled mankind has turned 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 breathing a sigh of relief. After all, he hadn't boasted and had finally achieved his goal of conquering Polignac's conjecture!
In the sea of consciousness, the enlightenment stele emitted a radiant light that expanded, nourishing Wu Tong's almost dry and tired brain like a downpour of rain from heaven, replenishing the energy consumed by Wu Tong's brain's high-speed operation over the past two days.
The light surrounding it has become richer again. It has changed from its initial state of being as thin as a veil and almost invisible. After Wu Tong's continuous learning and acquisition of knowledge, and several near-sudden progress in knowledge, he has verified major conjectures and difficult problems, and gained the nourishment of the power of knowledge. It has become the rich color of today, almost like cow's milk, which also represents 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.
Everything Wu Tong saw could assist him in conducting in-depth analysis and deduction of its nature. Of course, this ability was only at a very basic level, capable of only simulating and deducing data, and it relied on Wu Tong's accumulated knowledge.
However, for Wu Tong, there 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 produced, but it was still just a manuscript, and she still had to organize it into a complete report.
However, this didn't take much effort. I spent a 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.
Another night of moonset and sunrise passed. After a deep rest and some morning exercises, Wu Tong went downstairs to enjoy the sumptuous breakfast prepared by his family.
Golden fried dough sticks, plump and chewy, refreshing pickles, cut in half, egg yolks sizzling with red oil, homemade salted duck eggs, this is grandma's specialty.
A palm-sized, crispy pancake, sandwiched with layers of thinly sliced braised beef and a rice-oil-simmered eight-treasure porridge. Just looking at it makes one's heart flutter, and eating it is an even more heavenly delight.
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 happily when she saw the lively look between Wu Tong's brows, 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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