Prime Numbers in Math – Properties and Examples

Here you will learn what are prime numbers in math, its properties and method to check whether a number is prime or not.

Let’s begin –

What are Prime Numbers in Math ?

A natural number larger than unity is a prime number if it does not have other divisors except for itself and unity.

For example : 2, 3, 5, 7, 11 etc are all prime numbers.

Note : Unity (i.e. 1) is not a prime number.

Properties of Prime Number

1). The lowest prime number is 2.

2). 2 is the only even prime number.

3). The lowest odd prime number is 3.

4). The remainder when a prime number p \(\ge\) 5 is divided by 6 is 1 or 5. However, if a number on being divided by 6 gives remainder of 1 or 5 the number need not be prime.

5). The remainder of the division of the square of a prime number p \(\ge\) 5 divided by 24 is 1.

6). For prime numbers p > 3, \(p^2\) – 1 is divisible by 24.

7). If a and b are two odd primes then \(a^2 – b^2\) is composite. Also, \(a^2 + b^2\) is composite.

8). The remainder of the division of the square of a prime number p \(\ge\) 5 divided by 12 is 1.

Prime numbers between 1 to 100

The prime numbers between 1 to 1oo are : 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Shortcut Method to Check Number is Prime or Not

To check whether a number N is prime, adopt the following process.

1). Take the square root of the number.

2). Round of the square root to the immediately lower integer. Call this number z. For example if you have to check for 181, its square root will be 13… . Hence, the value of z, in this case will be 13.

3). Check for the divisibility of the number N by all prime numbers below z. If there is no prime number below the value z which divides N then the number N will be prime.

Example : The value of \(\sqrt{239}\) lies between 15 to 16. Hence take the value of z as 15.

Prime numbers less than 16 are 2, 3, 5, 7, 11 and 13, 239 is not divisible by any of these. Hence you can conclude that 239 is a prime number.

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