What is the meaning of prime number and composite number?

What is the meaning of prime number and composite number?

Prime number is also called prime number. It refers to the number in a natural number greater than 1 which can not be divided by other natural numbers except 1 and the integer itself. In other words, natural numbers with only two positive factors (1 and itself) are prime numbers. Numbers larger than 1 but not prime numbers are called composite numbers. 1 and 0 are neither prime nor composite numbers

What are the common characteristics of prime numbers and composite numbers
The common characteristics of prime and composite numbers are as follows
It means that as long as the number has the characteristic, it must be a prime or composite number, and the number without the characteristic must not be a prime or composite number
Factor:
The integer a can be divided by the integer B. A is called the multiple of B, and B is called the factor of A. the meaning of division here should include two aspects: one is that there is no remainder, and the other is that the quotient is an integer and is fixed (unique). We know that 0 is an even number. The definition of even number is that the number that can be divided by 2 is even, so 0 can be divided by 2, In other words, 2 is a factor of 0. We also know that the quotient of 0 divided by any non-zero integer is 0, so any non-zero integer is a factor of 0. The result of any non-zero integer divided by 0 does not exist, so 0 cannot be a factor of any non-zero integer. The result of 0 divided by 0 is any number, which is not fixed (not unique), so 0 cannot be a factor of 0, This also means that 0 cannot be a factor of any integer
Range:
In my opinion, it is meaningless to say that 1 is or is not a prime number if 1 is not defined in the scope of the concept of prime number. It is meaningful to say that 1 is or is not a prime number only if 1 is defined in the scope of the concept of prime number. If 1 is defined in the scope of prime number, now 1 is not a prime number, who can make it clear that 1 does not have the factor of 1 or does not have the factor of 1 itself
be careful! 0 has countless factors.
0 is a very important integer, everywhere, everywhere.
0 has no factor of its own.
I think 0 is neither a prime nor a composite number, 1 is a common prime, 2, 3, 5, 7, 11 They are unique primes, 4, 6, 8, 9, 10, 12 It's a sum. The basic components of number theory are equivalent to unique prime numbers.

According to your requirements: the common characteristics of prime and composite numbers: natural numbers that are not 1
2. Definition: for any integer a, B (B ≠ 0), there exists an integer C. If a = BC, then B (≠ 0) is called to divide a, or B is a factor of a, and a is a multiple of B
From 0 = B × 0, so any number (b) that is not 0 can be divided by 0, or any number (b) that is not 0 is a factor of 0, and 0 is a multiple of any number (b) that is not 0, "so any integer that is not 0 is a factor of 0", "0 cannot be a factor of 0", "0 cannot be a factor of any integer", "0 has countless factors" are correct;
A ≠ 0, there is no integer C, so that a = 0 × C, "so 0 can not be any factor of an integer that is not 0" is also correct;
3. We can define 1 as a prime or not. If we define 1 as a prime, then all natural numbers can be divided into two categories: prime and composite, and the cardinal numbers of the two categories are equal
All natural numbers are divided into three categories: prime numbers, composite numbers and unit numbers 1,1
On the surface, it is reasonable to define 1 as a prime, but it is not the case in reality. If 1 is defined as a prime, the concept of prime becomes meaningless
Prime numbers play the role of "atom" in the multiplication of integers. Apart from 1 multiplied by itself, prime numbers can not be expressed as the product of other two numbers. That is to say, prime numbers are "indivisible". Any integer can be expressed as the product of several prime numbers (atoms), and the decomposition is unique. If 1 is defined as a prime number, it will be very inconvenient, 15 = 3 × 5 = 1 × 3 × 5 = 1 × 1 × 3 × 5, The representation is not unique, even prime numbers can be decomposed, such as: 7 = 1 × 7, so 1 is defined as a prime number, which makes the concept of prime number meaningless. Therefore, it is not surprising that 1 is not regarded as a prime number, and 1 is not regarded as a prime number. For multiplication, 1 keeps the same number as any number operation, and any number except 1 does not have this characteristic, and prime numbers are just like "atoms" for multiplication, So it's no surprise that 1 is not a prime

Properties of prime numbers and composite numbers

A prime number is a factor with only one and itself
A composite number is a factor. Besides 1 and itself, there are other factors
For example:
13 = 1 × 13, so 13 is prime
12 12 = 1 × 12 12 = 2 × 6 12 = 3 × 4, so 12 is a composite number