From 1729 to 1764, Goldbach kept correspondence with Euler for 35 years. In the letter to Euler 1742 on June 7, Goldbach put forward a proposition:

1. Any even number greater than 2 is the sum of two prime numbers.

2. Any odd number greater than 5 is the sum of three prime numbers.

Since Goldbach put forward this conjecture, many mathematicians have been trying to conquer it, but they have not succeeded. Of course, some people have done some specific verification work, such as: 6 = 3+3, 8 = 3+5, 10 = 5+5 = 3+7, 12 = 5+7,14 = 7+7 = 3+/kloc. Someone looked up even numbers greater than 6 within 33× 108, and Goldbach conjecture (1) was established. But strict mathematical proof requires the efforts of mathematicians.

Several conjectures of Goldbach

Since then, this famous mathematical problem has attracted the attention of thousands of mathematicians all over the world. 200 years have passed and no one has proved it. There is no substantial progress. Goldbach conjecture has therefore become an unattainable "pearl" in the crown of mathematics. People's enthusiasm for Goldbach conjecture lasted for more than 200 years. Many mathematicians in the world try their best, but they still can't figure it out.

It was not until the 1920s that people began to approach it. 1920, the Norwegian mathematician Brown proved by an ancient screening method, and reached a conclusion that any even number greater than a certain big even number n can be expressed as the sum of two almost prime numbers, and these two almost prime numbers have at most 9 prime factors. (The so-called "almost prime number" refers to the odd number of prime factors (including the same and different) that does not exceed a fixed constant. For example, 15 = 3× 5 has two prime factors, and 27 = 3× 3× 3 has three prime factors. ) This conclusion is recorded as "9+9".

At present, the best result is proved by China mathematician Chen Jingrun in 1966, which is called Chen Theorem: "Any sufficiently large even number is the sum of a prime number and a natural number, and the latter is only the product of two prime numbers at most." This result is usually called (1+2).