The distribution of prime numbers is irregular and often confusing. For example, 10 1, 40 1, 60 1, 70 1 are all prime numbers, but the upper and lower 30 1(7*43) and 901(/.

Someone has done this calculation:12+1+41= 43, 2 2+2+4 1 = 47, 3 2+3+4 1 = 53 ...........................................................................'s formula holds up until n=39. But when n=40, the formula is invalid, because 40 2+40+41=1681= 41* 41.

Speaking of prime numbers, Goldbach conjecture and the famous "1+ 1" are indispensable.

Goldbach conjecture: (Goldbach conjecture)

All even numbers not less than 6 can be expressed as two prime numbers.

This question was put forward by the German mathematician C Goldbach (1690- 1764) in a letter to the great mathematician Euler on June 7th, 742, so it is called Goldbach conjecture. On June 30th of the same year, Euler replied that this conjecture may be true, but he could not prove it. Since then, this mathematical problem has attracted the attention of almost all mathematicians. Goldbach conjecture has therefore become an unattainable "pearl" in the crown of mathematics. "In contemporary languages, Goldbach conjecture has two contents, the first part is called odd conjecture, and the second part is called even conjecture. Odd number conjecture points out that any odd number greater than or equal to 7 is the sum of three prime numbers. Even conjecture means that even numbers greater than or equal to 4 must be the sum of two prime numbers. " (Quoted from Goldbach conjecture and Pan Chengdong)

Goldbach conjecture seems simple, but it is not easy to prove, which has become a famous problem in mathematics. In 18 and 19 centuries, all number theory experts did not make substantial progress in proving this conjecture until the 20th century. It is directly proved that Goldbach's conjecture is not valid, and people adopt "circuitous tactics", that is, first consider expressing even numbers as the sum of two numbers, and each number is the product of several prime numbers. If the proposition "every big 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" is recorded as "a+b", then the Coriolis conjecture is to prove that "1+ 1" holds.

1900, Hilbert, the greatest mathematician in the 20th century, listed Goldbach conjecture as one of the 23 mathematical problems at the International Mathematical Congress. Since then, mathematicians in the 20th century have "joined hands" to attack the world's "Goldbach conjecture" fortress, and finally achieved brilliant results.

In the 1920s, people began to approach it. 1920, the Norwegian mathematician Bujue proved by an ancient screening method that every even number greater than 6 can be expressed as (9+9). This method of narrowing the encirclement is very effective, so scientists gradually reduce the number of prime factors of each number from (99) until each number is a prime number, thus proving Goldbach's conjecture.

1920, Bren of Norway proved "9+9".

1924, Rademacher proved "7+7".

1932, Esterman of England proved "6+6".

1937, Ricei of Italy proved "5+7", "4+9", "3+ 15" and "2+366" successively.

1938, Byxwrao of the Soviet Union proved "5+5".

1940, Byxwrao of the Soviet Union proved "4+4".

1948, Hungary's benevolence and righteousness proved "1+c", where c is the number of nature.

1956, Wang Yuan of China proved "3+4".

1957, China and Wang Yuan successively proved "3+3" and "2+3".

1962, Pan Chengdong of China and Barba of the Soviet Union proved "1+5", and Wang Yuan of China proved "1+4".

1965, Byxwrao and vinogradov Jr of the Soviet Union and Bombieri of Italy proved "1+3".

1966, China and Chen Jingrun proved "1+2" [in popular terms, it means even number = prime number+prime number * or even number = prime number+prime number (Note: the prime numbers that make up even numbers cannot be even numbers, but only odd numbers. Because there is only one even prime number in the prime number, that is 2. )]。

The "s+t" problem refers to the sum of the products of S prime numbers and T prime numbers.

The main methods used by mathematicians in the 20th century to study Goldbach's conjecture are screening method, circle method, density method, triangle method and so on. The way to solve this conjecture, like "narrowing the encirclement", is gradually approaching the final result.

20 165438+20061October 23rd, the largest prime number in the world has been found to be as high as 22.33 million digits.