6 = 3 + 3, 8 = 5 + 3
10 = 5 + 5 , ………
100 = 97 + 3 102 = 97 + 5 ………
9 = 3 + 3 + 3, 1 1 = 5 + 3 + 3 ………
99 = 89 + 7 + 3, 10 1 + 89 + 7 + 5 , ………
So are these two conclusions true for all such even numbers and odd numbers? 1742 On June 7th, German mathematician Goldbach first raised the above question in his letter to Euler. On June 30th, Euler wrote back: "Any even number greater than 4 is the sum of two odd prime numbers. Although I can't prove it yet, I have no doubt that this is a completely correct theorem. " Because Euler was the greatest mathematician at that time, his self-confidence attracted many mathematicians to try to prove it, but there was no progress until the end of 19, which is the famous Goldbach conjecture.
The solution to this problem is to test each natural number and see if Goldbach conjecture holds for each number. But the difficulty is that there are infinite natural numbers, and no matter how many are verified, it cannot be concluded that the next number is still the same. In fact, some people have verified all even numbers as high as 3300000000000000, and still can't solve this problem. Therefore, a famous mathematician said, "Goldbach conjecture is as difficult as any unsolved mathematical problem." Some people compare Goldbach's conjecture to the jewel in the crown of mathematics. "
Mathematicians have made countless efforts to get this pearl. 1937, Soviet mathematicians proved that every big odd number can be expressed as the sum of three odd numbers. This big odd number is greater than the 4 million power of 10 (1 followed by 4 million zeros), and the largest known prime number is much smaller than this. But it is far from a conclusion, and it has not been proved whether odd numbers can be expressed as the sum of three odd prime numbers. So mathematicians adopt a step-by-step method to prove a problem similar to Goldbach's conjecture, that is, first prove that any positive integer greater than 4 can be expressed as the sum of C prime numbers (C is a constant). Along this road, mathematicians proved that:
C≤800000 ( 1930)，
C≤2208 ( 1935)，
C≤7 1 ( 1936)，
C≤67 ( 1937)，
C≤20 ( 1950)，
1956 yin wenlin of China proved that c≤ 18.
1937 Soviet mathematicians proved that the Goldbach problem is equivalent to c=2 for a large enough even number. But the proof from 4 to 2 is quite difficult. Obviously, this road is not completely smooth.
At the same time, mathematicians are still trying to take another road. That is to say, it is proved that every big even number can be expressed as the sum of several prime factors and several prime factors not exceeding B number. This proposition is called (a+b). In this way, Goldbach's conjecture basically proves that (1+ 1) is correct.
1920, the Norwegian mathematician Brown first proved (9+9), and since then, the work in this field has made continuous progress.
1957, China mathematician Wang Yuan proved (2+3).
1962, China mathematician Pan Chengdong proved it (1+5), and cooperated with Wang Yuan to prove it (1+4) in the same year. It was later proved (1+3).
1966, China mathematician Chen Jingrun proved it (1+2) and published it in 1973, which immediately caused a sensation in the international mathematics field. An English mathematician said that Chen Jingrun moved the mountain.
Although it is only one step from (1+2) to (1+ 1), the difficulty of this step is unbelievable. Many mathematicians believe that in order to prove (1+ 1), it is likely that new methods must be created, and the road ahead is impassable.