The Goldbach Conjecture

The Goldbach Conjecture is a well-known unsolved problem in number theory. Its core content is that any even number greater than 2 can be expressed as the sum of two prime numbers. For instance, 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, and so on.

The Goldbach Conjecture was proposed by the German mathematician Christian Goldbach in 1742. He first put forward this conjecture in a letter to the great mathematician Leonhard Euler. Euler restated it in a more concise form in his reply, namely, “Any even number greater than 2 can be written as the sum of two prime numbers.”

Although the statement of the conjecture is simple, its proof is extremely difficult. It touches upon one of the core concepts in mathematics – prime numbers, which are positive integers that can only be divided by 1 and themselves (such as 2, 3, 5, 7, etc.). If the conjecture is proven, it will have a profound impact on mathematical theory.

Although the Goldbach Conjecture has not been completely proven to date, mathematicians have made some significant progress:

Contribution of Chen Jingrun: In 1966, the Chinese mathematician Chen Jingrun proved the “1+2” proposition, that is, any sufficiently large even number can be expressed as the sum of a prime number and a semi-prime number. This achievement is regarded as an important milestone in the study of the Goldbach Conjecture.

Weak Goldbach Conjecture: In 2013, the mathematician Harald Helfgott announced the complete proof of the Weak Goldbach Conjecture, which states that any odd number greater than 7 can be expressed as the sum of three prime numbers.

The Goldbach Conjecture is not only an important topic in number theory but also has driven the development of mathematical research. It inspires people to explore infinite mathematical problems and promotes the innovation of mathematical tools such as the sieve method and circle method.

Although mathematicians have supported the conjecture through extensive verification, no complete proof or counterexample has been found to date. The Goldbach Conjecture remains a major challenge in the field of mathematics, attracting the exploration of countless mathematics enthusiasts and professionals.