C Program to display Prime Numbers between Two Intervals

To write a program to display Prime Numbers between Two Intervals we should know how to find a Number is Prime Number or Not?

To find a Number is Prime Number or Not, you can check out the following link:
C program to find a Number is Prime Number or Not

Program code to display Prime Numbers between Two Intervals:

/* Program to display Prime numbers between two Intervals */
#include<stdio.h>
#include<conio.h>
#include<math.h>

void main()
{
    int n, i, j, min, max, flag=0;
    clrscr();
    
    printf("\n Enter two numbers(Intervals) : ");
    scanf("%d%d",&min,&max);
    
    printf("\n The prime numbers between %d and %d are :",min,max);
    
    for(i=min+1;i<max;i++)
    {
        flag=0;
        
        for(j=2;j<=sqrt(i);j++)      //Loop to check whether 'i' (number) is divisible by any number between 2 and sqrt(i)
        {
            if(i%j==0)
            {
                flag=1;
                break;
            }
        }
        
        /* if condition to check and print if the Number is Prime Number */
        if (flag==0)
        {
            printf(" %d ",i);
        }
    }
    getch();
}

Working:

  • First the computer reads two numbers (Intervals) from the user.
  • Then using outer for loop the numbers between the intervals are take one by one.
  • Then using inner for loop it checks whether the number is prime number or not.
  • Then if condition is used to check and print if the number is prime number.
  • Thus all the prime numbers are printed.

Step by Step working of the above Program Code:

  1. Let us assume that a user enters the numbers as 5 and 20.
  2. It assigns the value of min=5 and max=20.
  3. It assigns the value of i=min+1 (ie. i=6) and the loop continues till the condition of the outer for loop is true.

3.1.  i<max    (6<20)    outer for loop condition is true

It assigns flag=0 , j=2

3.1.1.   j<=sqrt(i)    (2<=√6)    inner for loop condition is true

  i%j==0    (6%2==0)    if condition is true

It assigns flag=1

breaks the loop and comes out of the inner for loop

flag==0    (1==0)    if condition is false

So it goes for next iteration of outer for loop.

i++            (i=i+1)     So  i=7

3.2.  i<max    (7<20)    outer for loop condition is true

It assigns flag=0 , j=2

3.2.1.   j<=sqrt(i)    (2<=√7)    inner for loop condition is true

  i%j==0    (7%2==0)    if condition is false

j++            (j=j+1)     So  j=3

3.2.2.   j<=sqrt(i)    (3<=√7)    inner for loop condition is false

   It comes out of the inner for loop.

flag==0    (0==0)    if condition is false

So it prints 7 and goes for next iteration of outer for loop.

i++            (i=i+1)     So  i=8

3.3.  i<max    (8<20)    outer for loop condition is true

It assigns flag=0 , j=2

3.3.1.   j<=sqrt(i)    (2<=√8)    inner for loop condition is true

   i%j==0    (8%2==0)    if condition is true

It assigns flag=1

breaks the loop and comes out of the inner for loop

flag==0    (1==0)    if condition is false

So it goes for next iteration of outer for loop.

i++            (i=i+1)     So  i=9

3.4.  i<max    (9<20)    outer for loop condition is true

It assigns flag=0 , j=2

3.4.1.   j<=sqrt(i)    (2<=√9)    inner for loop condition is true

   i%j==0    (9%2==0)    if condition is false

j++            (j=j+1)     So  j=3

3.4.2.   j<=sqrt(i)    (3<=√9)    inner for loop condition is true

   i%j==0    (9%3==0)    if condition is true

It assigns flag=1

breaks the loop and comes out of the inner for loop

flag==0    (1==0)    if condition is false

So it goes for next iteration of outer for loop.

i++            (i=i+1)     So  i=10

3.5.  i<max    (10<20)    outer for loop condition is true

It assigns flag=0 , j=2

3.5.1.   j<=sqrt(i)    (2<=√10)    inner for loop condition is true

   i%j==0    (10%2==0)    if condition is true

It assigns flag=1

breaks the loop and comes out of the inner for loop

flag==0    (1==0)    if condition is false

So it goes for next iteration of outer for loop.

i++            (i=i+1)     So  i=11

3.6.  i<max    (11<20)    outer for loop condition is true

It assigns flag=0 , j=2

3.6.1.   j<=sqrt(i)    (2<=√11)    inner for loop condition is true

   i%j==0    (11%2==0)    if condition is false

j++            (j=j+1)     So  j=3

3.6.2.   j<=sqrt(i)    (3<=√11)    inner for loop condition is true

   i%j==0    (11%3==0)    if condition is false

j++            (j=j+1)     So  j=4

3.6.3.   j<=sqrt(i)    (4<=√11)    inner for loop condition is false

   It comes out of the inner for loop.

flag==0    (0==0)    if condition is false

So it prints 11 and goes for next iteration of outer for loop.

i++            (i=i+1)     So  i=12

  1. Similarly the outer for loop gets executed till the value of i<max (ie. i<20) and prints the prime numbers.
  1. Thus program execution is completed.

Output:

prime numbers

TO DOWNLOAD THE PROGRAM CODE : CLICK HERE

 

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