That is, the number of mersenne prime is;

Find the sum of the general formula of the sequence and the first few terms from the known sequence

Solution: The sequence is geometric progression, so the common ratio is all.

That is, the arithmetic function has the following properties:

( 1):

(2): If it is a (Mei Sen) prime number, it must be a prime number;

(3): In time, if it is a prime number, there must be a mersenne prime; Where there are prime numbers, there must be mersenne prime; Just like playing word games! There is actually a causal relationship.

(4): When is mersenne prime, it needs to be calculated separately, so

Suppose the formula is established in, it is a prime number, indicating the number of mersenne prime between; and

So, when,

And: and the corresponding

Both are established; I don't know if it can hold on. If established, there will be:

When, the number of mersenne prime is, that is, both are true.

Note: Mathematical induction is used to assume that it is true at that time, and it is also true if it cannot be deduced. But if we assume that time is true by backward induction, we can deduce that time is true. Because it is known to be true, backward induction adds four initial conditions of backward recursion on the basis of forward induction, which is the basic condition for both forward and backward induction to be true.

Inverse mathematical induction;

If a set containing positive integers has the property that if it contains integers, it also contains integers, and all of them are in it, then this set must be a set containing positive integers.

Establish the elements of reverse mathematical induction;

It is more strict than forward induction, with four more recursive starting conditions. Omitted in positive induction, strictly speaking, it cannot be omitted. Because when we guess that the conclusion is wrong, we only consider the recursive condition (basic step), but it is also true to assume that it is true but can be deduced in the inductive step. There are many such examples, such as (mistakes):

Basic steps: when the result is true, because it is not considered.

Induction step: suppose the result is true for me and true for me.

Therefore, positive induction should also be considered, because the conclusion of speculation is correct and omitted.

From this, we can draw the following conclusions:

1): If it is a prime number, it can be deduced that it must be a prime number and it is all prime numbers, then it is all prime numbers. It is concluded that mersenne prime is infinite.

If the tower-shaped prime number is obtained at the top of the tower, it is infinite;

If it is not a prime number, it has factors, so it is not a prime number;

So: the number of towers at the top of the tower is prime. After that, all numbers are prime numbers.

Basic pyramid prime number:

Derived from the pyramid prime number has an infinite variety, such as:

2): It only contains a finite number of prime numbers (even numbers with the middle as the base, so it is impossible to have the same prime number); Therefore, a single contains only a finite number of prime numbers.

There are only a limited number of prime numbers, and even numbers are odd or even, so it is impossible to have the same prime number and find the prime number at the same time;

Especially when the number of mersenne prime is (if established).

If reverse mathematical induction is established, it can solve many difficult problems and open a new world.

I wonder if it has anything to do with the fact that there is no radical solution to the equation of degree 5 or above.

Unfortunately, experts think that this article has no academic value and that Zhou Haizhong's guess is impossible. This shows the level of domestic experts!

Edited on 20 17-03- 16.