As a mathematics major, Lu Zhou certainly knew what a Mersenne prime was. After all, when it comes to Mersenne primes, one cannot help but mention a great Chinese mathematician and his "Law of Distribution of Mersenne Primes" published in 1992, which turned Mersenne primes into a formula that could be expressed mathematically, commonly known internationally as the Zhou Conjecture.

Before that, although British mathematician Shanks, French mathematician Trottot, German mathematician Berlihat, Indian mathematician Ramanujan, and American mathematician Gillis had all proposed conjectures respectively, their conjectures had one thing in common: they were all proposed as approximate expressions and were not satisfactory in terms of their closeness to the actual situation.

However, the precise formula of the Zhou Conjecture is very concise, that is, when 2^(2^n) < P < 2^(2^(n+1)), there are 2^(n+1) - 1 Mersenne primes that are prime numbers.

Sounds simple, doesn't it?

I could do it too, right?

Yet, just this one conjecture remains unproven or refuted to this day and has become a famous mathematical problem, puzzling the entire mathematical community for more than twenty years.

However, like the Riemann Hypothesis, although it cannot be proven, it does not prevent later generations from assuming it to be true and applying it.

Of course, even with a precise calculation formula, even if the task of searching for treasures is handed over to computers, discovering Mersenne primes is still not an easy task.

As of now (2014), the mathematical community has discovered a total of 44 Mersenne primes.

As for what use Mersenne primes are?

It seems that there is no particular use.

If you must say, the RSA algorithm is one. Every time you shop online, you have to thank the large prime numbers hidden in the passwords that cannot be cracked.

Meanwhile, large prime numbers are also used to test computer performance. For instance, Intel uses the GIMPS program to verify its chips, and the SKYLAKE chip once had a bug discovered through this method. Moreover, it's rather meaningless to ponder whether mathematics is useful. Often, the motivation for mathematicians to take action isn't necessarily the economic benefits derived from solving an equation, but simply because it exists. To put it broadly, humanity cannot afford to only focus on the immediate trivialities; we must also have poetry and distance. However, Lu Zhou was not pleased. He didn't want any poetry or distance; what he wanted was precisely the here and now! And why, of all things, must it be the proof method for the Zhou Conjecture! Give me the Riemann Hypothesis instead! Or even the slightly less ambitious Bill Conjecture would do! Putting aside its academic value, the bounty for the Bill Conjecture has already reached one million dollars, offered by the renowned Texan banker Bill himself. As for the Zhou Conjecture, while many have attempted to prove it, it seems no one has offered a reward for it. Seeing a house potentially slip away like that, Lu Zhou's mood instantly soured. But on the bright side, even if it's just the Zhou Conjecture, proving it would still be a remarkable achievement to be remembered in the history of mathematics. As for material rewards, although there is no bounty for this conjecture, the university should not treat him unfairly, at least the scholarship for the next three years is assured. Isn't that sophomore Liu, who proved the Xietao Pan Conjecture in his second year, the best proof?

It is said that Nan Da University directly granted 1 million RMB, of which 500,000 was allocated for scientific research funds, and another 500,000 was used to improve living conditions. Jin Da University could at least rank within the top ten nationwide. Although its mathematics department was a bit weak, even for the sake of appearances, it couldn't be outdone by Nan Da University, which was outside the top ten, right? Thinking this way, Lu Zhou felt somewhat relieved. After calming down, he took a look at the proof process. Unlike the cola labeled as 'trash,' the proof method for the Zhou Conjecture, which belonged to the 'blueprint' category, was not concretely presented on paper or electronic files. Whenever he wanted to see it, he only needed to silently recite it in his mind, and the entire proof steps would directly emerge in his head. 'I can't understand it at all... It seems that just grasping this proof process will take some time.' Lu Zhou pondered in his mind how to smoothly present the proof process he had. First of all, it was useless to just memorize; he had to understand it himself. Secondly, he needed to package himself as a top student. Not to mention anything else, if you could solve a mathematical problem as difficult as the Zhou Conjecture, you couldn't possibly fail to get full marks in advanced calculus or mathematical analysis, right? Even if you carelessly lost one point on the paper, you would still need to score 99. However, Lu Zhou wasn't too worried about this. He had completely mastered the two courses of mathematical analysis and advanced algebra these past two days. University mentors generally wouldn't deliberately make things difficult for students, and the knowledge points examined were definitely all in the textbooks. The cooked duck wouldn't run away anyway, and as for the proof of the Zhou Conjecture... Lu Zhou planned to take it out after the summer vacation was over.

Over the course of these two months, he would make every effort to package himself as a true academic prodigy, maximizing the benefits he could obtain. It was essential to seek more discussions with mentors on academic issues. Achieving Math LV1 was a must. Staying on campus for the summer vacation was also necessary. He would also have to call his parents afterward; his next trip back home might be during the New Year. With the matter of rewards concluded, another question emerged in Lu Zhou's mind. Would the 'blueprints' obtained from the lottery be related to 'academic levels'? This question was crucial. Otherwise, why was it so coincidental that he didn't draw anything else but a damn 'proof question answer'? Why not the grand prize 'cosmic battleship'? Once this thought popped into his head, it lingered and grew more plausible the more Lu Zhou pondered. 'The priority is to raise the academic level, to quickly upgrade math to LV1, and unlock the upper limit of other subjects' LV1 levels. In the meantime, should I hoard the lottery opportunities? However, without using the lottery, the task list cannot be refreshed, so hoarding lottery opportunities isn't realistic...' He clearly remembered that after claiming the task reward, the task list turned gray. It wasn't until he used up both of his lottery chances that the options on the task list became selectable again. Regarding this, he could only know after several more lottery draws. If the prizes were 'proof question answers' for several consecutive times, then his guess would undoubtedly be correct. On another note, it seemed that a new task could be claimed. What could it be? With this in mind, Lu Zhou silently recited to himself. 'Open task list!'

A translucent holographic screen emerged in front of me. 【 Task 1: The Art of Milking the Situation Description: Milking the situation is also an art. Why bother to work hard in the laboratory when you can earn money while lying down? Requirement: Cleverly use the art of language to get your name on a scientific research project with millions of dollars in funding. Adhere to the principle of doing the least amount of work for the greatest gain, and achieve the highest merits with the least energy consumption. So, milk the situation as much as possible, young man! Reward: Gain disciplinary experience (the type of experience is determined by the project type, the numerical value of experience is positively correlated with the amount of research funding, and negatively correlated with the host's contribution to the project). One lottery chance (100% junk). 】 【 Task 2: Practice the Basics (Physics) Description: Rome wasn't built in a day, and neither was the edifice of science. Requirement: Solve 200 university physics problems (the problem set is provided by the system, tailored to the host's knowledge reserve). Reward: Difficulty coefficient of the problems * 2. 50 points. Item—Deep Learning Time (Category: Special. Effect: Within the effective time of 24 hours, reading books can enter a deep reading state, permanently mastering the learned knowledge points). 】 【 Task 3: Academia Begins with Papers Description: A paper is the foundation of scholarship. A scholar who can only write papers may not necessarily achieve great things in academia, but a scholar who cannot write papers definitely cannot achieve great things in academia. Please do not argue with the system about this point; the system is truth! 】

Now, publish an SCI paper and start your academic career! Requirement: Publish an SCI paper. Reward: Discipline experience (determined by the academic value of the paper, with a minimum of 100 experience). 200 points. One lottery chance (95% junk, 5% sample). Seeing the last task, Lu Zhou's expression became somewhat strange. The reward experience is determined by the academic value of the paper? If he were to publish the proof process of the Zhou's Conjecture in an SCI journal, he wondered how much experience it would bring. Thinking about it, this idea was quite tempting...