## Chapter 6: The Answer For A Proof Question

Of course, one would have to mention a famous Chinese mathematician when speaking about Mersenne prime numbers. In 1992, he published “Mersenne prime numbers distribution formula” and his paper was able to illustrate an equation for Mersenne prime numbers. It was then famously named “Zhou’s approximation”.

Previously, the British mathematician William Shanks, French mathematician Tartaglia, German mathematician Luders, Indian mathematician Ramanujan, and American mathematician Gillies had all speculated on this problem. Although they had a common theme, which was the approximation of the equation, the closeness of their research to the exact answer was unsatisfactory.

Zhou’s approximation formula was very simple. When 2^(2^n) < p < 2^(2^(n+1)), p has 2^(n+1)-1 prime numbers.

Simple, right?

Anyone could do this, right?

However, the equation had not been proven or disproved. It had become one of the most famous mathematical problems and had been troubling the mathematics community for over 20 years.

It was like Riemann’s conjecture. Even though it could not be proven, it did not stop people from using it.

Of course, even though there was an accurate way of using computers to discover Mersenne primes, it was still not an easy feat.

As of today, only forty-four Mersenne primes were discovered.

Was there any use for the Mersenne primes?

It seemed unlikely.

Strictly speaking, using the RSA algorithm, every time an online transaction went through, you would have to thank the unsolvable prime numbers that were hidden in the password. At the same time, large prime numbers were also used to test computer performances. For example, Intel used the GIMPS application to test the chips for bugs.

Anyway, to debate whether mathematics was useful was unmeaningful. Very often, the drives that motivated the mathematicians were not in monetizing the discovery, but merely because the problem was there.

At the end of the day, humans could not look purely at the short term gains but they had to also look at the long term gains.

However, Lu Zhou was not really willing. He did not care about the future. He wanted the gains now!

Also, why was it Zhou’s approximation proof! Why not Riemann’s Conjecture! Or even the lower level Birch’s conjecture would be okay!

Putting the academic value aside, Birch’s conjecture prize was already at one million U.S dollars. The prize money came from the well-known Texas banker Birch himself.

As for Zhou’s approximation, there were a lot of people that were attempting to prove it. However, there was no prize money attached if one solved it.

A potential chance to own a house just flew away and Lu Zhou no longer felt so good anymore.

However, he should look at the bright side. Even though it was only Zhou’s approximation, proving it would still give him some reputation in the mathematical world. Although there was no physical prize that was attached to the discovery, the university would not treat him shabbily either. Three years of scholarship should be guaranteed.

The sophomore who proved Ramsey’s theorem was the best example. Apparently, the University of Nanjing gave him a million dollars, half of which was used as funding for his research while the other half for his living expenses.

The University of Jin Ling is among the top 10 in the country. Even though their mathematics department is relatively weak, the University of Jin Ling should still give more money than the lower ranked University of Nanking, right?

After thinking about it, Lu Zhou felt slightly better.

He calmed down and started to look over the proof theorem.

It was different than the coke from the “garbage” category. Zhou’s approximation proof was categorized under “blueprint”. It was not printed on paper or as a digital file. When he wanted to read it, he just had to think about it and all the proof steps will appear in his brain.

“I can’t comprehend this at all… I guess I would have to spend quite a lot of time to understand this proof.”

Lu Zhou thought about how he would successfully extract the steps of the proof.

First of all, memorizing it was no use as he had to understand it.

Secondly, he had to portray himself as a genius.

Regardless, if one could solve a high level question such as Zhou’s approximation, one would need to at least be able to score full marks in high school maths, right? Even if one accidentally lost one mark, one would still need to get 99 marks.

Lu Zhou was not too concerned about it. It only took him two days to finish learning mathematical analysis and advanced algebra. The lecturers would not trick the students on purpose. They would only test what was in the syllabus.

Everything was already secured… Lu Zhou planned to present Zhou’s approximation proof after the summer holidays. In the next two months, in order to maximize his gains, he would try to make himself into a true genius.

He must find teachers to discuss the math problems with.

Level 1 mathematics was also a must.

The summer school was also a must.

He also had to call his parents as it could be New Year before his next family visit.

After getting his prizes, a question popped into Lu Zhou’s head.

Is the blueprint prize correlated with subject level?

This question was crucial.

Otherwise, why was he so unlucky and got a weird proof answer? As opposed to the first prize space battleship?

The theory was stuck in Lu Zhou’s head. The more he thought about it, the more likely it seemed.

“Ranking up a subject level is a priority. I should get mathematics level 1 ASAP in order to unlock other subjects’ level 1 limit. Before that, should I save my lucky draw tickets? But if I don’t utilize the lucky draw tickets, I can’t refresh the mission list. It’s not realistic to hoard the lucky draw tickets…”

He clearly remembered that after he got the mission prizes, the mission list turned gray. Only after using his lucky draw tickets did the mission list became selectable again.

The only way to know was to enter more lucky draws.

If the next consecutive prizes were all proof answers, his theory would be correct.

Anyways, he should be able to take on new missions.

What will it be?

Lu Zhou began to think.

“Open mission list!”

A semi-transparent screen appeared in front of him.

[

Mission 1: The art of profiting from laziness

Description: Profiting from laziness is also a form of art. If you can earn money while being lazy, why would you need to work hard?

Requirements: Utilize the art of language and get your name on a million dollar science research project. Use as little effort as possible to gain the maximum merit. Try to be lazy, young one!

Reward: Subject experience points (Subject determined by research project type, amount of experience points is positively correlated with research project funding, negatively correlated with the amount of effort used). One lucky draw ticket (100% garbage).

]

[

Mission 2: Practice fundamental skills

Description: Rome wasn’t built in a day, neither was the skyscraper of science.

Requirements: Solve 200 university level physics exercise questions (Questions are provided by the system and created with respect to the user’s current knowledge).

Rewards: Question difficult level x 2. 50 general points. Item: Immersive learning hours (Type: special. Effect: 24 hours. Within a valid time frame, immersive learning is enabled when reading books. Permanent mastery of knowledge gained.)

]

[

Mission 3: Academic starts from theses

Explanation: Theses are the backbone of academia. An academician that can write a thesis might not be successful, but an academician that cannot write a thesis definitely won’t be successful. Do not argue with the system about this. The system is definitely right! Publish a scientific thesis and start your academic career!

Requirements: Publish a scientific thesis.

Rewards: Subject experience points (determined by thesis value with a minimum of 100 points). 200 general points. One lucky draw ticket (95% garbage, 5% samples).

]