Prime numbers have many unique properties:
The (1) prime p has only two divisors: 1 and p.
(2) Basic theorem of elementary mathematics: Any natural number greater than 1 is either a prime number itself or can be decomposed into the product of several prime numbers, and this decomposition is unique.
(3) The number of prime numbers is infinite.
(4) The number formula of prime numbers is an irreducible function.
(5) If n is a positive integer, then there is at least one prime number between and.
(6) If n is a positive integer greater than or equal to 2, there is at least one prime number between n and.
(7) If the prime number p is the largest prime number not exceeding n (), then.
(8) Among all prime numbers greater than 10, the unit number is only 1, 3, 7, 9.
Extended data:
Inverse prime number:
Reading backwards and forwards are prime numbers. Such as 1949 and 949 1, 301and 1 103, 1453 and 354 1, etc. Non-repeated inverse prime numbers refer to inverse prime numbers whose numbers are not repeated. Such as 13 and 3 1, 17 and 7 1, 37 and 73, 79 and 97, 107 and 70 1, etc.
Cyclic descending prime number and cyclic ascending prime number;
A prime number (9 is connected with 1-9) consists of nine numbers connected in reverse or positive order. Such as: 43,1987,76543,23,23456789, 12345679 1. The largest number found now is a 28-bit number:123456789123456789123456791.
A number consisting of some special numbers:
For example, 3 1, 33 1, 333 1, 3333 1, 33333 1, 33333 1 are all qualitative. Especially famous is the prime number composed of 1 If the number consisting of n consecutive 1 is denoted as Rn, R2 = 1 1 is a prime number. Later, it was found that R 19, R23, R3 17 were all prime numbers.
The study of prime numbers is the oldest and most basic part of number theory, which focuses on a large number of seemingly extremely simple problems that are difficult to solve for decades or even hundreds of years. Besides several famous problems such as Goldbach conjecture, there are still many unsolved problems.
References:
Baidu encyclopedia-prime number