#### Abstract

Open Access Research Article Article ID: AMP-5-162

# The continuity of prime numbers can lead to even continuity (Relationship with Gold Bach’s conjecture)

## Xie Ling*

N continuous prime numbers can combine a group of continuous even numbers. If an adjacent prime number is followed, the even number will continue. For example, if we take the prime number 3, we can get an even number 6. If we follow an adjacent prime number 5, we can get even numbers by using 3 and 5: 6, 8 and 10. If a group of continuous prime numbers 3, 5, 7, 11, ..., P, we can get a group of continuous even numbers 6, 8, 10, 12,..., 2n. Then if an adjacent prime number q is followed, the Original group of even numbers 6, 8, 10, 12,..., 2n will be finitely extended to 2(n + 1) or more adjacent even numbers. My purpose is to prove that the continuity of prime numbers will lead to even continuity as long as 2(n + 1) can be extended. If the continuity of even numbers is Discontinuous, it violates the Bertrand Chebyshev theorem of prime Numbers.

Because there are infinitely many prime numbers: 3, 5, 7, 11,...

We can get infinitely many continuous even numbers: 6, 8, 10, 12,...

Get: Gold Bach conjecture holds.

2020 Mathématiques Subjectif Classification: 11P32, 11U05, 11N05, 11P70.

Research ideas:

If the prime number is continuous and any pairwise addition can obtain even number continuity, then Gold Bach’s conjecture is true.

Human even number experiments all get (prime number + prime number).

I propose a new topic: the continuity of prime numbers can lead to even continuity.

I designed a continuous combination of prime numbers and got even continuity.

If the prime numbers are combined continuously and the even numbers are forced to be discontinuous, a breakpoint occurs.

It violates Bertrand Chebyshev's theorem.

It is proved that prime numbers are continuous and even numbers are continuous.

The logic is: if Gold Bach's conjecture holds, it must be that the continuity of prime numbers can lead to the continuity of even numbers.

Image interpretation: turn Gold Bach’s conjecture into a ball, and I kick the ball into Gold Bach’s conjecture channel.

There are several paths in this channel and the ball is not allowed to meet Gold Bach’s conjecture conclusion in each path.

This makes the ball crazy, and the crazy ball must violate Bertrand Chebyshev's theorem.

Keywords:

Published on: Dec 2, 2022 Pages: 171-179