"Then, substitute equation ② and transform it, and then..."
Lin Xiao took the last few steps of his own. Until the end, he raised his brows slightly and looked at the final result he had arrived at.
[When g(x)>f(x)>t(x)(x∈N+)..., the f(x)/pn term of the Mersenne number is a prime number. 】
At this point, Lin Xiao's final result is completed.
He successfully predicted the distribution of the Mersenne sequence, and was accurate to each item. In addition, he also proved that there are infinite Mersenne primes, because x belongs to the set of all positive integers, and obviously the positive integers are infinite.
If there are multiple Mersenne primes, there are infinitely many Mersenne primes.
And through the relationship he finally obtained, people today can easily judge whether it is a Mersenne prime number by simply substituting all the known prime numbers into it.
Of course, it seems meaningless to say this. After all, we are still limited to the largest prime number, and the largest prime number currently discovered is also the largest Mersenne prime number discovered. It was discovered on December 26, 2017, which is 2^
77232917-1, when calculated according to the decimal system, it has nearly 23 million digits.
However, this is not the truth, because we are still not sure whether one or even two of the largest Mersenne prime numbers we have discovered and the second largest Mersenne prime number have slipped through the net. In the same way, we cannot guarantee that the third Mersenne prime number has slipped through the net.
Is there anything missing 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. In the Internet Mersenne Prime Search (GIMPS), a volunteer mathematics research project, among the 51 Mersenne primes discovered so far, there are many
The middle Mersenne primes 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 have slipped through the net will be easily discovered, and we will also be able to easily discover larger prime numbers than currently
, after all, the current maximum Mersenne prime number is based on the prime number 77232917, and humans have obviously discovered many prime numbers larger than 77232917, such as the prime number 82589933. If you use it to calculate, you may be able to
Has mankind discovered a larger prime number? (2^82589933-1 is the largest Mersenne prime number discovered in December 2018.)
"Huh~"
Putting down the pen in his hand, Lin Xiao had a satisfied smile on his face, he finally got it done.
It is now July 12, and there are still 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 time is a little tight, they are just simple tasks. Compared with solving this problem, they are much simpler. After all, it took Lin Xiao nearly a month to complete this problem.
.
Lin Xiao stretched and took a sip of water.
At this time, the system's pleasant sound also sounded at the right time.
"Congratulations to the host for determining the distribution pattern of Mersenne prime numbers. Considering the host's various performances in the research, the reward is: +300 mathematical experience, +10 truth points, and 15 hours of sage status."
"Congratulations to the host for reaching level 3 in mathematics! The current experience value is: 246/1000."
After hearing these two notifications, Lin Xiao's eyes suddenly lit up, and he actually directly added 300 experience points, plus 10 truth points.
The 15-hour sage state surprised him even more. It was a good thing that could directly increase brain development by 50%. After experiencing it last time, he had already experienced the kind of understanding of the world.
It feels like, now that his brain is more developed, won’t it be even more improved by then?
"By the way, I have reached level 3 in mathematics. Should I also be rewarded for my brain development?"
Lin Xiao suddenly remembered this matter.
The system also happened to respond: "Mathematics is upgraded to level three, and the brain development degree is rewarded by 0.4%."
There is actually 0.4%?
Lin Xiao was very surprised when he heard this number, 0.4%, which is equivalent to 13% of his current brain development!
It really deserves to be a level 3, it’s awesome!
Just as she was pleasantly surprised, Lin Xiao suddenly felt her head feel heavy and she felt dizzy.
This is a side effect that occurs when the degree of brain development is greatly improved. If the degree of improvement is low, like last time it was only increased by 0.05%, Lin Xiao will feel a little cool in the brain.
But these are not big problems. After Lin Xiao calmed down for a while, he felt that his brain began to become clearer, as if he had entered a true sage state.
Of course, what flashed through his mind was not the three ultimate questions of philosophy, but various mathematical problems.
Now, his understanding of mathematics has also improved to a considerable extent. If he studied the previous work at his current level, he estimated that he would be able to complete it in less than ten days and a half, instead of spending as much time as before.
It took more than twenty days to get it done.
After sighing with emotion about the current situation, Lin Xiao began to sort out his results and input them into the computer.
However, during the process of sorting, thanks to the improvement of his brain development and mathematics level, he observed the final conclusion, suddenly raised his eyebrows, and thought of something in his mind.
Then he took out his pen and calculated again on the scratch paper. Soon, he got a new inference.
[When 2^2^(x+1)>p>2^2^x, Mp=2^(x+1)-1, (x∈N+)]
After writing this, he wrote the four words "Zhou's guess" at the back, and then wrote two more words.
【Certificate completed.】
This conjecture named after a Chinese person was proved by his hands. From now on, it will also be called Zhou's theorem.
Although it was verified based on Lin Xiao's accurate prediction, this theorem has been overwritten by Lin Xiao's results.
But this is also the effort of the predecessors in the Chinese mathematics community 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 Mersenne prime distribution predicted by other foreign mathematicians.
In a way, this also means that from now on, two Chinese mathematicians will be ahead of countless people in the foreign mathematics community in the field of Mersenne prime numbers.