Among the mathematical conjectures related to prime numbers in history, the most famous one is Goldbach's conjecture.

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

1. Any even number not less than 4 can be the sum of two prime numbers (for example, 4 = 2+2);

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

This is the famous Goldbach conjecture in the history of mathematics. Obviously, the second guess is the inference of the first guess. So it is enough to prove one of the two conjectures.

biographical notes

On June 30th of the same year, Euler made it clear in his reply to Goldbach that he was convinced that both Goldbach's conjectures were correct theorems, but Euler could not prove them at that time. Because Euler was the greatest mathematician in Europe at that time, his confidence in Goldbach's conjecture influenced the whole mathematics field in Europe and even the world. Since then, many mathematicians are eager to try and even devote their lives to proving Goldbach's conjecture. However, until the end of 19, there was still no progress in proving Goldbach's conjecture. The proof of Goldbach's conjecture is far more difficult than people think. Some mathematicians compare Goldbach's conjecture to "the jewel in the crown of mathematics".

Let's start with 6=3+3, 8=3+5, 10=5+5, ...,100 = 3+97 =1+89 =17+89. In the 20th century, with the development of computer technology, mathematicians found that Goldbach conjecture still holds true for larger numbers. However, natural numbers are infinite. Who knows if a counterexample of Goldbach's conjecture will suddenly appear on a sufficiently large even number? So people gradually changed the way of exploring problems.

1900, Hilbert, the greatest mathematician in the 20th century, listed Goldbach conjecture as one of the 23 mathematical problems at the International Mathematical Congress. Since then, mathematicians in the 20th century have "joined hands" to attack the world's "Goldbach conjecture" fortress, and finally achieved brilliant results.

Proof process

The main methods used by mathematicians in the 20th century to study Goldbach's conjecture are screening method, circle method, density method, triangle method and so on. The way to solve this conjecture, like "narrowing the encirclement", is gradually approaching the final result.

1920, the Norwegian mathematician Brown proved the theorem "9+9", thus delineating the "great encirclement" that attacked "Goldbach conjecture". What is this "9+9"? The so-called "9+9", translated into mathematical language, means: "Any large enough even number can be expressed as the sum of two other numbers, and each of these two numbers is the product of nine odd prime numbers." Starting from this "9+9", mathematicians all over the world concentrated on "narrowing the encirclement", and of course the final goal was "1+ 1".

1924, the German mathematician Redmark proved the theorem "7+7". Soon, "6+6", "5+5", "4+4" and "3+3" were captured. 1957, China mathematician Wang Yuan proved "2+3". 1962, China mathematician Pan Chengdong proved "1+5", and cooperated with Wang Yuan to prove "1+4" in the same year. 1965, Soviet mathematicians proved "1+3".

1966, Chen Jingrun, a famous mathematician in China, conquered "1+2", that is, "any even number large enough can be expressed as the sum of two numbers, one of which is an odd prime number and the other is the product of two odd prime numbers." This theorem is called "Chen Theorem" by the world mathematics circle.

Thanks to Chen Jingrun's contribution, mankind is only one step away from the final result of Goldbach's conjecture "1+ 1". But in order to achieve this last step, it may take a long exploration process. Many mathematicians believe that to prove "1+ 1", new mathematical methods must be created, and the previous methods are probably impossible.