From Almighty Scholar to Chief Scientist

Chapter 88
"Then, after substituting formula ②, transform it, and then..."

Lin Xiao carried out his last few steps, until the end, he raised his brows slightly, looking at the final result he had drawn.

[When g(x)>f(x)>t(x)(x∈N+)..., the f(x)/pn item of the Mersenne number is a prime number.】

So far, Lin Xiao's final result has been completed.

He successfully predicted the distribution of the Mersenne sequence, and it was accurate to each item. In addition, he also proved that there are infinitely many Mersenne prime numbers, because x belongs to the set of all positive integers, and obviously positive integers are infinite If there are many, then there are infinitely many Mersenne primes.

And through this relational formula he finally obtained, people today can easily judge whether it is a Mersenne prime number by substituting all known prime numbers into it.

Of course, it seems meaningless to say this, after all, we are still limited by the largest prime number, and the largest prime number discovered so far is also the largest Mersenne prime number discovered on December 2017, 12, which is 26^ 2-77232917, when calculated according to the decimal system, it has nearly 1 million digits.

However, the truth does not say this, because we still cannot be sure whether there is one or even two slipping fish between the largest Mersenne prime and the second largest Mersenne prime we have discovered. Similarly, we cannot guarantee that the first Mersenne prime Whether there is a fish that slipped through the net between the second largest Mersenne prime number and the third largest Mersenne prime number.

In fact, in the past, mathematicians often found such fish that slipped through the net. Among the 51 Mersenne primes discovered so far, there are more than The few Mersenne primes in the middle were all discovered after a larger Mersenne prime was discovered.

Now, Lin Xiao has completely solved this problem. As long as people have enough time, all the fish that escaped the net will be easily discovered, and we will also be able to easily discover prime numbers that are larger than the current ones. , after all, the current largest Mersenne prime number is the prime number 77232917 as the index, and the prime number larger than 77232917, humans have obviously discovered many, such as the prime number 82589933, if it is used to calculate, it may be able to make How about humans discovering a larger prime number? (2^82589933-1 is the largest Mersenne prime discovered in December 2018.)
"Whoo~"

Putting down the pen in his hand, a satisfied smile appeared on Lin Xiao's face, and it was finally done.

It is now July 7th, and there are three days before the deadline. In these three days, he will organize these things on the computer, then translate them into English, and submit them to the National Congress of Mathematicians.

Although the time is a bit tight, it is just some simple tasks. Compared with solving this problem, it is much simpler. After all, it took Lin Xiao nearly a month to complete this problem. .

Stretching, Lin Xiao took a sip of water.

At this time, the pleasant voice of the system also sounded at the right time.

"Congratulations to the host for determining the distribution of Mersenne primes. Considering the various performances of the host in the research, rewards: Mathematical experience +300, truth points +10, sage state for 15 hours."

"Congratulations to the host's mathematics level reaching level 3! The current experience value is: 246/1000."

Hearing these two notifications, Lin Xiao's eyes lit up immediately, and he actually added 300 experience points directly, and 10 truth points in addition.

And the 15-hour sage state surprised him even more. This is a good thing that can directly increase the development of the brain by 50.00%. After experiencing it last time, he has already experienced the feeling of understanding the world, and Now that his brain is more developed, won't it improve even more?

"By the way, I've passed Level [-] in Mathematics. Shouldn't the degree of brain development be rewarded?"

Lin Xiao suddenly remembered this matter.

The system also just responded: "Mathematics is promoted to the third level, and the brain development degree is rewarded by 0.4%."

There is actually 0.4%?

Hearing this number, Lin Xiao was very pleasantly surprised, 0.4%, which is equivalent to 13% of his current brain development rate!
It's really worthy of being a level 3, it's awesome!
Just as he was pleasantly surprised, Lin Xiao suddenly felt a heavy head, feeling dizzy.

This is a side effect when the development of the brain is greatly improved, and if the degree of improvement is low, like the last time it only increased by 0.05%, Lin Xiao will feel a little cool in the brain.

But these are not big problems. After Lin Xiao slowed down for a while, he felt that his brain began to clear up, as if he had entered a state of true sage.

Of course, what flashed through his mind was not the ultimate philosophical question, but various mathematical problems.

Now, his understanding of mathematics has also improved to a considerable extent. If he studies the previous work at the current level, he estimates that he will be able to finish it in ten days and a half months, instead of spending as much as before. It took more than 20 days to get it done.

After feeling a little bit about the current state, Lin Xiao began to sort out his results and input them into the computer.

However, in the process of sorting out, thanks to the improvement of brain development and mathematics level, he observed the final conclusion, raised his brows suddenly, and thought of something in his mind.

Then he took out a pen and calculated on the draft paper, and soon, he got a new inference.

【当2^2^(x+1)>p>2^2^x时，Mp=2^(x+1)-1，（x∈N+）】

At this point, he wrote the four words 'Zhou's Guess' on the back, and then wrote two more words.

[The certificate is completed. 】

This conjecture named after the name of the Hua people has also been proved in his hands. From then on, it will also be called Zhou's theorem.

Although it was verified based on Lin Xiao's precise prediction, this theorem has been covered by Lin Xiao's results.

But this is also the effort of seniors in Huaguo's mathematics field in the field of mathematics. Although it is not as perfect as the distribution formula given by Lin Xiao, it is at least much more accurate than the distribution of Mersenne prime numbers predicted by other foreign mathematicians.

In a way, this also means that from now on, there are two mathematicians belonging to Huaguo, who are ahead of countless people in foreign mathematics circles in the field of Mersenne prime numbers.

(End of this chapter)