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Chapter 397 The proof of Zhou’s conjecture, the birth history of a generation of scholars!

The original title is as follows…

“Prime numbers are also called prime numbers. They are numbers that can only be divisible by themselves and 1, such as 2, 3, 5, 7, 11, etc.”

“2300 years ago, the ancient Greek mathematician Euclid proved that there are infinitely many prime numbers in the book “The Elements of Geometry”, and proposed that a small number of prime numbers can be written as “2^P-1” (where the exponent P is also a prime number) In the form of, this prime number is called “Mersenne prime” (Mersenneprime).”

“So far.”

“Humans have only discovered 48 Mersenne primes. Mersenne primes are rare and charming, so they are known as the “Pearl of the Sea”.”

“At the same time, the distribution of Mersenne primes is sparse and dense, and extremely irregular. In addition, it is not known whether there are infinitely many Mersenne primes. Therefore, exploring the important properties of Mersenne primes-the distribution law seems to be more difficult than finding new Mersenne primes.”

“The current known law guess is that it was proposed by Dongyun mathematician Lao Zhou in 1976…”

“When 2^(2^n)<p<2^(2^(n+1)), 2^(n+1)-1 of Mp are prime numbers."

"Lao Zhou also made an inference based on this: when p<2^(2^(n+1)), Mp has 2^(n+2)-n-2 prime numbers."

"(Note: p is a prime number; n is a natural number; Mp is a Mersenne number)."

"Sp: Try to prove or disprove the guess?"

"…"

above.

This is what is recorded in the notebook.

There is still a very long following, involving some related proof methods, which have been variously demonstrated, and will be omitted for the time being.

Again……

If the average person sees this proof question, it is estimated that they will be dizzy and cramp immediately, and will pass out.

Just because…

This is really Zhou's conjecture!

Also called the guess of the distribution of Mersenne prime numbers.

The Mersenne prime conjecture, twin prime conjecture, Goldbach conjecture, ABC conjecture, and Riemann conjecture are also called the five major conjectures in prime numbers.

Although Zhou's guess is only a guess on the law of Mersenne's prime number, and the expression seems very simple.

But to prove or disprove the speculation.

That difficulty is not trivial.

Anyway, countless people in mathematics have tried to prove that even if they rack their brains, they still get nothing.

Now I don’t know which black hand put the notebook in front of Jiang Nan again, can he prove it?

If it were in the past, it's really hard to say.

But now?

This possibility is still there.

When he opened his notebook, he was not surprised but rather happy, and quickly found a table to sit down, eager to try.

In other words…

He hasn't seen such a difficult proof question for a long time, comparable to the previous twin prime conjecture.

Although there are challenges.

But his favorite is the challenge.

Can't say it.

He has to prove it today.

"Solution: first resolve Zhou's guess as: when 2^(2^(n−1))<p<2^(2^n), 2^n-1 of Mp are prime numbers, and πMp^(2^ n)-πMp^(2^2(n−1))=2^n-1……(a).”

"That is, when p<2^(2^n), the number of πMp^(2^(2^n)) Mersenne primes is 2^(n+1)-n-1."

"…"

"Assume first…"

"Check again…"

"Reverse mathematical induction can be used…"

[If a set containing positive integers has the following properties, that is, if it contains the integer k+1, it also contains the integer k, and 1, 2, 3, 4, and 5 are all in it, then this set must be so positive A collection of integers. 】

"The essentials for the establishment of reverse mathematical induction…"

"(1) Basic steps: (recursive starting conditions) when n=1, 2, '3, 4, 5 are all true (have the same properties)."

"(2) Inductive step: (assuming the derivation condition) when the assumption n=k+1 is established, it can be deduced that n=k is established."

"(3) Then n to ∞ are all true."

[Sp: Reverse induction is more rigorous than forward induction, because it has four more recursive starting conditions. 】

"…"

"Borrowing the hypothesis, using the reverse induction method, through a number of inference steps (108-step bottoming), we can finally draw a conclusion: there are infinite prime numbers."

"…"

"call!"

I don't know how long it took.

Jiang Nan stopped writing slightly, exhaled, and pinched the center of his eyebrows with his thumb and index finger.

Um!

A huge notebook.

He has already written most of it densely.

But has the Zhou's conjecture that everyone thought has baffled countless people been proven?

How can it be?

Whether it is the three major problems in modern mathematics, the seven major problems in the millennium, or other conjectures, any conjecture that can become a difficult conjecture and prove any one will win the Fields Medal out of ten.

nature!

It would never be so easy.

If it is an ordinary person, such as the author Lao Cang, except for one solution above, none of the above can be understood (•̥́ˍ•̀ू).

Even readers with superior intelligence can only understand 70% to 80% (´｡✪ω✪｡｀).

However……

This is actually just to prove that the Mersenne prime number is infinite, and it only involves a premise of Zhou's conjecture.

Zhou's conjecture is a guess on the distribution of Mersenne prime numbers, or a formula summary. This has not yet begun.

Gee!

This is simply scary.

Even Jiang Nan, our pig's feet, feels a little tired, it's really too much mental exhaustion.

but……

This is exactly the charm of mathematics, isn't it?

If it is really that simple, it won't make countless people yearn for it, and go forward and explore it.

There was a saying that was good.

Whether it is a guess or a problem, it is equivalent to the red apples of a young man.

It hangs high above everyone's heads, unchanged forever, and can be seen by countless mathematicians, just waiting for a tall man to stand on tiptoe and pick it up in his hands.

And this process of tiptoeing and picking is the process of seeking truth, which will fascinate countless people.

At least……

Jiang Nan is very fascinated.

Although he felt tired, he only twisted his eyebrows, then picked up the pen and paper and continued to dry.

"Swipe!"

The pen walks the dragon and the snake, the speed is very fast.

I saw page after page of notebook blank, covered by densely packed formulas.

For the layman, this is definitely a celestial book or a mantra, which cannot be understood by humans. The numbers and symbols that jump between Jiang Nan's pen and paper are sorrows that everyone will never understand.

But for Jiang Nan.

This process of searching for the truth and reshaping nature is really cool, it can be said to be hearty.

He is tired and wants to stop.

But a devil's scream and confusion sounded in the ear all the time: "No, no, just a little bit, just a little bit too close, don't stop, continue, I can still bear it…"

Tell me…

Is it possible to stop at such a critical moment?

Real man, you can't stop!

Jiang Nan only feels that the whole person is going to be sublimated, completely forgetting all things in the world, and only pen and paper are left in his hands.

Time passed by every minute.

I don't know how long it took.

He put down his pen still unfinished.

Um!

It's not that he has thoroughly proved Zhou's conjecture.

It was this huge notebook, which was densely written again, and there was no place to write.

So much so that Jiang Nan had to stop.

Then……

Jiang Nan leaned on the chair and exhaled, feeling that he was going to collapse ๐·°(৹˃̵﹏˂̵৹)°·๐.

And at the same time.

I only heard a sound of "gurgling", which came from his stomach, the kind that was almost starving.

"There is no sun and moon in the question, and I don't know when I am hungry."

"Life is nothing more than eating and sleeping, but I actually forgot such an important thing."

"In this way, I really have a generation to learn magic, no wonder I will become a pig's feet, hahaha!"

"(ಡωಡ)hiahiahia!!!"

"…"

sp: Stay up late for two days and can’t hold it anymore. It’s a change today, take a long time off, and make up ✧٩(ˊωˋ*)و✧ tomorrow.