What is a prime number?

prime number is a concept in mathematics, that is, a non-zero natural number whose common factor of two or more integers is only 1. Two nonzero natural numbers whose common factor is only 1 are called coprime numbers. Prime numbers have the following theorems:

1. Two nonzero natural numbers whose common factor is only 1 are called prime numbers; For example: 2 and 3, the common factor is only 1, which is a prime number;

2. Positive integers whose greatest common factor is only 1 are called prime numbers;

3. Two different prime numbers are coprime numbers;

4, 1 and any natural number are coprime. Two different prime numbers are coprime. A prime number and a composite number, which are coprime when they are not multiples. The coprime of two complex numbers without the same prime factor;

5. Any two adjacent numbers are coprime;

6. The probability that two positive integers are coprime (the greatest common divisor is one) is 6/π 2.

Extended data:

According to the definition of coprime numbers, some laws can be summarized, which can be used to quickly judge whether a group of numbers are coprime.

1. Two different prime numbers must be coprime numbers. For example, 7 and 11, 17 and 31 are prime numbers.

2. Two consecutive natural numbers must be prime numbers. For example, 4 and 5, 13 and 14 are prime numbers.

3. Two adjacent odd numbers must be prime numbers. For example, 5 and 7, 75 and 77 are prime numbers.

4, 1 and all other natural numbers must be prime numbers. For example, 1 and 4, 1 and 13 are prime numbers.

5. The larger of the two numbers is a prime number, and these two numbers must be prime numbers. For example, 3 and 19, 16 and 97 are prime numbers.

6. The smaller of the two numbers is a prime number, while the larger number is a composite number and not a multiple of the smaller number. These two numbers must be prime numbers. For example, 2 and 15, 7 and 54 are prime numbers.

7. If a large number is more than 1 or less than 2 times the decimal number, these two numbers must be prime numbers. For example, 13 and 27, 13 and 25 are prime numbers.

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