In the letters 1 and Goldbach 1742 to Euler, Goldbach put forward the following conjecture: any integer greater than 2 can be written as the sum of three prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler and asked him to help him prove it, but until his death, Euler could not prove it. Because the convention that "1 is also a prime number" is no longer used in mathematics, the modern statement of the original conjecture is that any integer greater than 5 can be written as the sum of three prime numbers. (n>5: When n is even, n=2+(n-2) and n-2 is even, it can be decomposed into the sum of two prime numbers; When n is odd, n=3+(n-3) and n-3 is even, it can be decomposed into the sum of two prime numbers), and Euler also put forward another equivalent version in his reply, that is, any even number greater than 2 can be written as the sum of two prime numbers. Today's popular conjecture is said to be Euler's version. Any sufficiently large even number of a proposition can be expressed as the sum of a number that does not exceed one prime factor and another number that does not exceed b prime factors. A+B. 1966 Chen Jingrun proof 1+2 holds, that is, any sufficiently large even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number.

2. The common conjecture today is the Euler version, that is, any even number greater than 2 can be written as the sum of two prime numbers, which is also called "strong Goldbach conjecture" or "Goldbach conjecture about even numbers".

3. It can be inferred from Goldbach's conjecture about even numbers that any odd number greater than 7 can be expressed as the sum of three odd prime numbers. The latter is called "weak Goldbach conjecture" or "Goldbach conjecture on odd numbers". If the Goldbach conjecture about even numbers is right, then the Goldbach conjecture about odd numbers will also be right. In May 20 13, Harold Horovgott, a researcher at Paris Teachers College, published two papers, announcing that the weak Goldbach conjecture was completely proved.