**Prime numbers** are the natural numbers that have **just two different dividers**: 1 and himself.

Examples:

1) **2** have only the dividers **1** and **2**, therefore **2** It's a prime number.

2) **17** have only the dividers **1** and **17**, therefore **17** It's a prime number.

3) **10** have the dividers **1, 2, 5** and **10**, therefore **10** **no** It's a prime number.

*Comments:***1 is not a prime number**, because he has only one divider that is himself.**2 **is the only prime number that is even.

Numbers that have more than two dividers are called **compound numbers**.*Example*: 15 has more than two dividers => 15 is a compound number.

## Recognition of a prime number

To know if a number is prime, we divide that number by prime numbers 2, 3, 5, 7, 11, etc., until we have:

- or a division with zero remainder (and in this case the number **not cousin**),

- or a division with **lower quotient** that the divisor and the **nonzero rest**. In this case the number **it's cousin**.

**Examples:**

1) The number 161:

- not even, so not divisible by 2;
- 1 + 6 + 1 = 8, so it is not divisible by 3;
- does not end in 0 or 5, so it is not divisible by 5;
- by 7: 161/7 = 23, with zero remainder, so 161 is divisible by 7, and therefore
**no**It's a prime number.

2) The number 113:

- not even, so not divisible by 2;
- 1 + 1 + 3 = 5, so it is not divisible by 3;
- does not end in 0 or 5, so it is not divisible by 5;
- by 7: 113/7 = 16, with remainder 1. The quotient (16) is still greater than the divisor (7).
- by 11: 113/11 = 10, with remainder 3. The quotient (10) is smaller than divisor (11), and furthermore the remainder is nonzero (the remainder is 3), so
**113 is a prime number**.