Composite number refers to the number divisible by other numbers (except 0) except 1 and itself in natural numbers.
Complex numbers within 50 are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 2/kloc.
The prime numbers within 50 are: 2,3,5,7, 1 1, 13, 17,19,23,29,31,37,4.
Extended data:
Complex attribute:
1, all even numbers greater than 2 are composite numbers.
2. In all odd numbers greater than 5, all numbers with 5 are composite numbers.
3. Except 0, all natural numbers with 0 are composite numbers.
4. All natural numbers with numbers 4, 6 and 8 are composite numbers.
5. The smallest (even) complex number is 4 and the smallest odd complex number is 9.
6. 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)
Properties of prime numbers:
The number of prime numbers is infinite. There is a classic proof in Euclid's Elements of Geometry. It uses a common proof method: reduction to absurdity. The concrete proof is as follows: Suppose there are only a limited number of prime numbers, which are arranged as p 1, p2, ..., pn from small to large, and let n = P 1× P2×...× PN, then is it a prime number?
If it is a prime number, it should be greater than p 1, p2, ..., pn, so it is not in those hypothetical prime numbers.
1, 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 number 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.
2. 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.
References:
Baidu Encyclopedia -Prime Baidu Encyclopedia-Sum