Goldbach conjecture;

1742 On June 7, the German mathematician Goldbach put forward a bold guess in a letter to the famous mathematician Euler:

Any odd number not less than 3 can be the sum of three prime numbers (for example, 7=2+2+3, when 1 was still a prime number).

On June 30th of the same year, Euler wrote back another version of Goldbach's conjecture: any even number can be the sum of two prime numbers (for example, 4=2+2. 1 was still a prime number).

This is the famous Goldbach conjecture in the history of mathematics. Obviously, the former is the inference of the latter. So we only need to prove the latter to prove the former. So we call the former weak Goldbach conjecture (which has been proved) and the latter strong Goldbach conjecture. Since 1 is no longer classified as a prime number, these two conjectures become:

Any odd number not less than 7 can be written as the sum of three prime numbers; Any even number not less than 4 can be written as the sum of two prime numbers.

Extended data:

Goldbach conjecture proves misunderstanding;

There are four methods to study Goldbach conjecture: almost prime number, exceptional set, small variable three prime number theorem and almost Goldbach problem.

Almost prime numbers are positive integers with almost no prime factors. Now let n be an even number. Although it cannot be proved that n is the sum of two prime numbers, it is enough to prove that it can be written as the sum of two almost prime numbers, that is, N=A+B, where a and b are prime numbers with almost no prime factor.

Use "a+b" to express the following proposition: every big even number n can be expressed as A+B, where the number of prime factors of A and B does not exceed A and B respectively. Obviously, Goldbach's conjecture can be written as "1+ 1". The progress in this direction is obtained through the so-called screening method.

The screening method proves that "1+2" has come to an end, and this road is obviously impassable.

The proof process of folk science is as follows: 2N is any big even number, and A is the largest prime number before 2N. Then 2N can be written as an array of (1, 2n- 1) (2, 2n-2) (3, 2n-3) ... (n, 2N-N). It is also said that the combinations that are not homogeneous prime numbers in this array can be screened by screening method, and as long as the remaining combinations are greater than 0, it is proved to be successful. The idea is simple.

First, filter the first number in the combination, leaving (3, 2n-3) (5, 2n-5) (7, 2n-7)...(A, 2N-A) to ensure that the first number in the combination is even, but the first number can be filtered and the last number cannot.

Baidu Encyclopedia-Three Mathematical Conjectures in the World