Any even number greater than 2 can be written as the sum of two prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler 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 can be expressed as the sum of a number with no more than one prime factor and a number with no more than b prime factors, and the proposition is called "a+b". 1966 Chen Jingrun proved that "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".

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Study history

Hua was the first mathematician in China who engaged in Goldbach conjecture. From 1936 to 1938, he went to England to study, studied number theory under Hardy, and began to study Goldbach conjecture, which almost verified all even conjectures.

From 65438 to 0950, after returning from the United States, Hua organized a seminar on number theory at the Institute of Mathematics of China Academy of Sciences, and chose Goldbach conjecture as the topic of discussion. Wang Yuan, Pan Chengdong, Chen Jingrun and other students who attended the seminar made good achievements in proving Goldbach's conjecture.

1956, Wang Yuan proved "3+4"; In the same year, the mathematician A.V. Noguera Dov of the former Soviet Union proved "3+3"; 1957, Wang Yuan proved "2+3"; Pan chengdong proved "1+5" in 1962; 1963, Pan Chengdong, Barba En and Wang Yuan all proved "1+4"; 1966, Chen Jingrun proved "1+2" after making new and important improvements to the screening method.

Baidu encyclopedia-Goldbach conjecture