The queen of natural science is mathematics, and Goldbach conjecture is the jewel in the queen's crown.

1On June 7, 742, Goldbach wrote to Euler and put forward the famous Goldbach conjecture: take any odd number, such as 77, it can be written as the sum of three prime numbers, that is, 77 = 53+17+7; Take odd numbers.

For example, 46 1 can be expressed as 46 1=449+7+5, which is also the sum of three prime numbers. 46 1 can also be written as 257+ 199+5, which is still the sum of three prime numbers. There are many examples, that is, it is found that "any odd number greater than 5 is the sum of three prime numbers."

1742 On June 30th, Euler wrote back to Goldbach. This proposition seems correct, but he can't give a strict proof. At the same time, Euler put forward another proposition: any even number greater than 2 is the sum of two prime numbers. But he also failed to prove this proposition.

Extended data

Goldbach conjecture three prime theorems

If even Goldbach conjecture is correct, so is odd Goldbach conjecture. You can think about this problem in reverse. As we all know, odd number n can be expressed as the sum of three prime numbers. If it can be proved that one of the three prime numbers is very small, for example, the first prime number can always take 3, then the Goldbach conjecture of even numbers is proved.

This thought prompted Mr. Pan Chengdong to study a triple prime number theorem with small qualitative change in 1959, that is, when he was 25 years old. This small qualitative change does not exceed the θ power of n.

It is necessary to prove that θ can take 0, that is, this small qualitative change is bounded, and thus the even Goldbach conjecture is deduced. Mr. Pan Chengdong first proved that θ can be 1/4. After a long time, there was no progress in this field until Professor Zhan Tao advanced Mr. Pan's theorem to 7/ 1995. This number is already relatively small, but it is still greater than 0.

Baidu encyclopedia-Goldbach conjecture