# Smallest two-digit prime number

### What is a Prime Number?

The natural numbers that are greater than 1 and having only two factors are called as prime numbers. There are two factors of a prime number in which one factor is '1' and another factor is the number itself. So, a prime number can only be divisible by 1 and itself.

### The smallest two digit prime number

The smallest two-digit number is 11. It has only two factors that are '1' and '11' itself. The next two-digit prime number after 11 is 13, and the prime number previous to 11 is 7.

Although the smallest two-digit number is 10, but it has more than two factors, and it also cannot be expressed in the form of the 6n + 1 or 6n -1, so it cannot be considered as a prime number. But 11 satisfy all conditions of a prime number, so it is the smallest two-digit prime number.

Except 2 and 3, every prime number can either be expressed in the form of 6n + 1 or 6n - 1. So, let's try to express 11 in these forms.

If we consider n as 2, so 11 can be written in the form of 6n - 1.

6 (2) - 1 = 11 (where n = 2)

So, 11 is a prime number.

In order to check whether the number is prime or not, we can follow the below steps -

• First, we have to write the factors of the given number.
• Then, we have to count the found factors.
• And if there are exactly two factors of the given number, then the number is prime. Otherwise, the number is composite.

### Properties of prime numbers

There are some properties of the prime numbers that are listed as follows -

• The smallest prime number is 2, which is the only even prime number. Except 2, all prime numbers are odd.
• Even positive integers greater than 2 can be expressed as the sum of two prime numbers.
• Two prime numbers are always co-prime to each other. When two numbers do not have a common factor other than 1 are co-prime numbers. Co-prime numbers are also called as 'mutually prime' or 'relatively prime'. Some of the examples of co-prime are (2, 3), (8, 15), (11, 17), (21, 22), etc.
• Except prime numbers 2 and 3, every prime number can either be written in the form of 6n - 1 or 6n + 1, where n is a natural number.
• A prime number cannot be negative, as according to the definition of a prime number, a number greater than 1 and can only be divided by 1 and itself, is called as a prime number.

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