A, Goldbach's guess:
/kloc-in the 8th century, the German mathematician Goldbach accidentally discovered that every even number not less than 6 is the sum of two odd prime numbers. Such as 3+3 = 6; 1 1+ 13=24。 He tried to prove his discovery, but failed many times.
1742, Goldbach turned to Euler, the most authoritative Swiss mathematician in the world at that time, and put forward his own conjecture. Euler quickly wrote back that this conjecture must be established, but he could not prove it.
Someone immediately looked up an even number greater than 6 until 330000000. The results show that Goldbach's conjecture is correct, but it can't be proved. So this conjecture that every even number not less than 6 is the sum of two prime numbers (referred to as "1+ 1") is called "Goldbach conjecture".
Second, the practical significance:
The practical significance of Goldbach's conjecture is that in the process of proving Goldbach's conjecture, some new problem-solving methods may appear, which is very important as a tool for mathematics and so on. Moreover, for the later application of human computer programs, biotechnology, military science and aerospace will have application fields.
Historical evolution and research methods of Goldbach conjecture;
I. Historical evolution:
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.
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 proved "3+4"; In the same year, mathematicians in the former Soviet Union proved "3+3"; 1957, Wang Yuan proved "2+3"; 1966, Chen Jingrun proved "1+2" after making new and important improvements to the screening method.
The difficulty in proving Goldbach's conjecture is that any prime number that can be found does not hold true in the following formula.
Second, research methods:
1, almost prime number: almost prime number is a positive integer with few prime factors.
2. Exception set: Take a big integer X on the number axis, and then look forward from X for even numbers that make Goldbach's conjecture untenable, that is, exceptional even numbers.
3. Three prime number theorem: It is known that odd number n can be expressed as the sum of three prime numbers. If we can prove that one of the three prime numbers is very small, for example, the first prime number can always take 3, then we also prove the Goldbach conjecture of even numbers.