For example: 2,3,5,7, 1 1, ...

The prime number p has only two divisors: 1 and p.

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.

The number of prime numbers is infinite.

The extended data 1, the number greater than 1 and its twice must have at least one prime number (that is, within the interval (a, 2a)).

2. There is a prime arithmetic progression of any length.

3. An even number can be written as the sum of two composite numbers, and each composite number has at most 9 prime factors. (Norwegian mathematician Brown, 1920)

4. Even numbers must be written as prime numbers plus composite numbers, in which the number of factors of composite numbers has an upper bound. (Renee, 1948)

5. Even numbers must be written as a prime number plus a composite number consisting of at most five factors. Later, some people called this result (1+5) (Pan Chengdong, China, 1968).

6. A sufficiently large even number must be written as a prime number plus a composite number consisting of at most two prime factors. Short for (1+2)