How to Find Prime Numbers?

If a number is given and you are asked whether it is a prime number or not. What shall you do? How will you know? Do you know how to find prime numbers? So here in this article, we will be discussing what is a prime number, how to find prime numbers easily, and how to check prime numbers.

  • Prime numbers are the numbers which have only two factors, the number itself and 1. So we have to find such numbers which have only two factors. We will be studying various methods to find prime numbers, how to check prime numbers, and table for prime numbers 1 to 200. 

What is the Prime Number?

A prime number is an integer greater than one and can be divisible by only itself and one i.e it has only two factors. Zero, one, and numbers less than one are not considered as prime numbers.

A number having more than two factors are referred to as composite numbers. The smallest prime number is 2 because it is divisible by itself and 1 only.

Finding Prime Numbers Using Factorization

The most common method used to find prime numbers is by factorization method. 

The steps involved in finding prime numbers using the factorization method are:

  • Step 1: First let us find the factors of the given number( factors are the number which completely divides the given number)

  • Step 2: Then check the total number of factors of that number

  • Step 3: Hence, If the total number of factors is more than two, it is not a prime number but a composite number.

For Example: Take a number 45. Is it a prime number?

Factors of 45 are 5 x 3 x 3

Since the factors of 45 are more than 2 we can say that 45 is not a prime number but a composite number.

Now, if we take the example of 11. The prime factorization of 11 is 1 x 11. You can see here, there are two factors of 11. Hence, 11 is a prime number.

Methods to Find Prime Numbers

Prime numbers can also be found by the other two methods using the general formula. The methods to find prime numbers are:


Method 1:

Two consecutive numbers which are natural numbers and prime numbers are 2 and 3. Apart from 2 and 3, every prime number can be written in the form of 6n + 1 or 6n – 1, where n is a natural number.

For example:

6(1) – 1 = 5

6(1) + 1 = 7

6(2) – 1 = 11

6(2) + 1 = 13

6(3) – 1 = 17

6(3) + 1 = 19…..so on


Method 2:

To find the prime numbers greater than 40,the general formula that can be used is n2+ n + 41, where n are natural numbers  0, 1, 2, ….., 39

For example:

(0)2 + 0 + 0 = 41

(1)2 + 1 + 41 = 43

(2)2 + 2 + 41 = 47

(3)2 + 3 + 41 = 53 

(4)2 + 2 + 41 =  59…..so on 


Note: These both are the general formula to find the prime numbers. But values for some of them will not yield a prime number.

Table of Prime Numbers 1 to 200

Here is the list of prime numbers from 1 to 200. This table will help you to find any prime numbers 1 to 200.

List of Prime numbers from 1 to 200 

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

101

103

107

109

113

127

131

137

139

147

151

157

163

167

173

179

181

191

193

197

199




Memorize this list of prime numbers from 1 to 200 and you can easily identify whether any number is prime or not.

Points to be Noted

  • Numbers having even numbers in one’ place cannot be a prime number.

  • Only 2 is an even prime number; all the rest prime numbers are odd numbers.

  • To find whether a larger number is prime or not, add all the digits in a number, if the sum is divisible by 3 it is not a prime number.

  • Except 2 and 3, all the other prime numbers can be expressed in the general form as    6n + 1 or 6n - 1, where n is the natural number.

Solved Examples

Example 1: Is 19 a Prime Number or not?

Solution:

We can check if the number is prime or not in two ways.

Method 1:

The formula for the prime number is 6n + 1

Let us write the given number in the form of 6n + 1.

6(3) + 1 = 18 + 1 = 19

Method 2: 

Check for the factors of 19

19 has only two factors 1 and 19. 

Therefore, by both the method we get 19 is a prime number.


Example 2: Is 53 is a prime number or not?

Solution:

Method 1:

To know the prime numbers greater than 40, the below formula can be used.

n2 + n + 41, where n = 0, 1, 2, ….., 39

Put n= 3

32 + 3 + 41 = 9 + 3 + 41 = 53


Method 2:

53 has only factors 1 and 53.

So, 53 is a prime number by both the methods.


FAQ (Frequently Asked Questions)

1. Check if number is prime.

The most common method used to check the prime numbers is by factorization method. 

The steps involved to check prime numbers using the factorization method are:

  • Step 1: First let us find the factors of the given number( factors are the number which completely divides the given number)

  • Step 2: Then check the total number of factors of that number

Step 3: Hence, If the total number of factors is more than two, it is not a prime number but a composite number.

2. How to calculate prime numbers?

Answer: Prime numbers can also be found by the other two methods using the general formula. The methods to find prime numbers are:

Method 1:

Two consecutive numbers which are natural numbers and prime numbers are 2 and 3. Apart from 2 and 3, every prime number can be written in the form of 6n + 1 or 6n – 1, where n is a natural number.

For example:

6(1) – 1 = 5

6(1) + 1 = 7

6(2) – 1 = 11

6(2) + 1 = 13

6(3) – 1 = 17

6(3) + 1 = 19…..so on

Method 2:

To find the prime numbers greater than 40,the general formula that can be used is n2+ n + 41, where n are natural numbers  0, 1, 2, ….., 39

For example:

(0)2 + 0 + 0 = 41

(1)2 + 1 + 41 = 43

(2)2 + 2 + 41 = 47

(3)2 + 3 + 41 = 53 

(4)2 + 2 + 41 =  59…..so on

3. Is 1 a prime number or composite number?

1 is neither a prime number or a composite number because 1 is divisible by only itself, thus it has only 1 factor. Hence it contradicts both the definition of a prime number and composite number. They both have more than two factors.

What is the difference between prime numbers and composite numbers?

A prime number has only two factors that is the number itself and one, while a composite number has more than two factors. 

A prime number is divisible by only 1 and by itself, while the composite number is divisible by all its factors.

For example, 2 is a prime number it is divisible by 1 and 2 itself

9 is a composite number, it has three factors 1, 3, and 9 and it is divisible by all its factors.