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. Some positive integers whose greatest common factor is only 1 are called prime numbers;
3. Two different prime numbers are prime numbers;
4. 1 is coprime with any natural number. Two different prime numbers are coprime. A prime number and a composite number 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 1) is 6/π 2.
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According to the definition of prime numbers, some laws can be summarized, which can be used to quickly judge whether a group of numbers are prime numbers.
1, two different prime numbers must be coprime numbers. For example, 7 and 1 1, 17 and 3 1 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.
All natural numbers such as 4, 1 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 one of the two numbers is a prime number, and the larger one is a composite number, 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 the larger number is twice the decimal number, it is 1 or less than 1. These two numbers must be prime numbers. For example, 13 and 27, 13 and 25 are prime numbers.
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