A natural number greater than one that is divisible by only 1 and itself, is known as a prime number. A prime number has no divisor other than 1 and itself. In other words, if a number "x" is a prime number than it has to be greater than 1 and is divisible by only 1 and x.
For example: 7 is a prime number because it is greater than 1 and is divisible only by 1 or 7.
9 is not a prime number, since it is divisible by 3.
Few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 ...........
The property of a number to be prime is known as primality.
Properties of Prime Numbers
Prime numbers have few important properties which are described below:
- There are infinitely many prime numbers.
- 1 and 0 are not categorized as prime numbers.
- There is no even prime number other than "2", because even numbers except 2 are divisible by 2 and hence are not considered as prime numbers.
- There is no prime number that ends in 5 and is greater than 5, because a number greater than 5 that ends in 5, is divisible by 5 and hence it is not a prime number.
- A prime gives zero remainder, only when divided by 1 or itself.
- The natural numbers greater than 1 and are not prime, are known as composite numbers.
- Every natural number can be represented in the form of product of prime numbers which is known as prime factorization. Prime factors for a particular number are unique.
- The set of prime numbers is a subset of natural numbers as well as integers and hence it is a subset of real numbers too.