2. A composite number refers to a number in a natural number that can be divisible by other numbers except 1 and itself (except 0).

3. The nature of prime numbers: if it is a composite number, because any composite number can be decomposed into the product of several prime numbers; The greatest common divisor of n and N+ 1 is 1, so it is impossible to be divisible by p 1, p2, pn, so the prime factor obtained by this complex number decomposition is definitely not in the assumed prime set. Therefore, whether the number is a prime number or a composite number, it means that there are other prime numbers besides the assumed finite number of prime numbers. So the original assumption doesn't hold water. In other words, there are infinitely many prime numbers. Other mathematicians have given some different proofs. Euler proved by Riemann function that the sum of reciprocal of all prime numbers is divergent, Ernst Cuomo proved more succinctly, and harry Furstenberg proved by topology.

4. Properties of composite numbers: All even numbers greater than 2 are composite numbers. Of all odd numbers greater than 5, 5 digits are composite numbers. Except 0, all natural numbers with 0 bits are composite numbers. All natural numbers with units of 4, 6 and 8 are composite numbers. The minimum (even) composite number is 4 and the minimum odd composite number is 9. Every composite number can be written as the unique form of the product of prime numbers, that is, the factorization of prime factors. (fundamental theorem of arithmetic)