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Prime Numbers - How to find prime number in c program?

In this tutorial, we are going to know about, how we can find prime numbers when the user enters the range.

for example :

Let's suppose the range is 10 - 100, then we have to find the prime numbers between them.

So, Let get started.

Program to find Prime Number :

 #include<stdio.h>  
 #include<conio.h>  
 int main(){  
 int lower_limit , upper_limit,flag;  
 printf("Enter the lower limit & upper limit");  
 scanf("%d%d",&lower_limit,&upper_limit);  
 for(int i= lower_limit ;i<=upper_limit ; i++){  
   flag =0;  
   for(int j =2 ;j<=i/2;j++){  
    if(i%j==0){  
     flag ++;  
     break;  
    }  
   }  
   if(flag==0 && i != 1){  
   printf("%d " ,i);  
   }  
  }  
 return 0;  
 }  

Output :

Prime Numbers - How to find prime numbers in C program?
Output of prime numbers in a range of 1 - 500

Explanation :

The program above find prime number between some range entered by user and print's the prime number found between this range.

Currently , We are using Nested for loop for this operation.

In the first part of the loop i,e first for loop , we initialized 'i' with lower limit and compare i< = upper_limit because we have to go from lower limit to upper limit .

For example :

let suppose we have to check prime number between 1 - 100 then we have to start with 1 then we have to move forward like 2 then 3, 4, 5 ......, 100 to judge the number one by one whether they are prime or not.

Moving on to next step we are initializing flag with 0 then second for loop starts.

In second for we initialized 'j' with 2 because from definition of prime number we know :


 " Prime Numbers are the number that has only 2 factors: 1 and themselves."


therefore if a number is divisible by 2 is not a prime number.

Moving forward we compare j<=i/2 after this we are dividing 'i' by 'j' to get remainder.

If it is 0 then we are increasing flag value with one and then break (to break second for loop).

When loop breaks we compare flag 0 & i don't equal to 1 if it is true then we print the number.

Why j<=i/2 ? :

Consider an example if we want to know whether 15 is prime or not? , then what we do?

we must divide it from 2 to 7 to check the remainder is zero or not because after 7, dividing 15 with the numbers next 7 we always get remainder greater than 0 then there is an increment in the value of flag leading to a wrong answer.


Prime Numbers Summary :

So ,this is the complete tutorial to find prime number in c program .

What we conclude from tutorial that we must use nested loop.

The first loop must start from lower limit and end's to upper limit the second loop starts from 2 and end's at half of current position of lower limit.

Then dividing them to get the remainder if remainder is zero then print the number .

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