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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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