Twin prime numbers refer to prime number pairs with a difference of 2, such as 3 and 5, 5 and 7, 1 1 and 13. This conjecture was formally put forward by Hilbert in the eighth topic of the report of the International Congress of Mathematicians in 1900. It can be described as follows: there are infinitely many prime numbers P, so that P+2 is a prime number. A pair of prime numbers (p, p+2) are called twin prime numbers.

1849, Alfonso de Polignac put forward a general conjecture: for all natural numbers k, there are infinite prime pairs (p, P+2K). The case of k = 1 is the twin prime conjecture.

Basic introduction

The conjecture of twin prime numbers is a famous unsolved problem in number theory. This conjecture has a long history; In the famous report of mathematician Hilbert at 1900 international congress of mathematicians, it is listed as the eighth of 23 "Hilbert problems", which can be described by "there are infinitely many prime numbers P, and for each P, the number P+2 is also a prime number".

Twin prime numbers are a pair of prime numbers with a difference of 2. For example, 3 and 5, 5 and 7, 1 1 3, 100 16957 and 100 16959 are all twin prime numbers. The prime number theorem shows that when a prime number tends to infinity, it tends to become scarce. Twin prime numbers have the same trend as prime numbers, and this trend is more obvious than prime numbers.

Because of the high popularity of the twin prime conjecture and its connection with Goldbach conjecture, many academic and mathematical enthusiasts try to prove it. Some people claim to have proved the twin prime conjecture. However, there is no proof that can be tested by professional mathematicians.

In 1849, Polignac put forward a more general conjecture: for all natural numbers k, there are infinite prime pairs (p, p+2k). The case of k = 1 is the twin prime conjecture. This pair of prime numbers (p, p+2) is called twin prime numbers. Mathematicians think this conjecture is correct.

In May of 20 13, Zhang's paper Bounded Distance between Prime Numbers was published in Mathematical Yearbook, which solved the problem that puzzled the mathematical community for a century and a half, and proved the weakening of the conjecture of twin prime numbers, that is, it was found that there were infinitely many prime number pairs with differences less than 70 million. This is the first time to prove that the distance between infinite pairs of prime numbers is less than a fixed value.