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C Program to Check Whether a Number is Prime or not

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  • Difficulty Level : Easy
  • Last Updated : 17 Oct, 2022
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Given a positive integer N. The task is to write a C program to check if the number is prime or not

Prime Number in C Language

Definition

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few prime numbers are {2, 3, 5, 7, 11, ….}

The idea to solve this problem is to iterate through all the numbers starting from 2 to sqrt(N) using a for loop and for every number check if it divides N. If we find any number that divides, we return false. If we did not find any number between 2 and sqrt(N) which divides N then it means that N is prime and we will return True. 
Why did we choose sqrt(N)? 
The reason is that the smallest and greater than one factor of a number cannot be more than the sqrt of N. And we stop as soon as we find a factor. For example, if N is 49, the smallest factor is 7. For 15, smallest factor is 3.
Below is the C program to check if a number is prime: 

C




// C program to check if a
// number is prime
  
#include <math.h>
#include <stdio.h>
int main()
{
    int n, i, flag = 1;
  
    // Ask user for input
    printf("Enter a number: \n");
  
    // Store input number in a variable
    scanf("%d", &n);
  
    // Iterate from 2 to sqrt(n)
    for (i = 2; i <= sqrt(n); i++) {
  
        // If n is divisible by any number between
        // 2 and n/2, it is not prime
        if (n % i == 0) {
            flag = 0;
            break;
        }
    }
  
    if (n <= 1)
        flag = 0;
  
    if (flag == 1) {
        printf("%d is a prime number", n);
    }
    else {
        printf("%d is not a prime number", n);
    }
  
    return 0;
}

Output

Enter a number: 11
11 is a prime number

Time Complexity: O(n1/2)
Auxiliary Space: O(1)

Method 2 : Optimized Approach using Wilsons theorem with O(N) complexity

If   ((n-1)! + 1) % n == 0  then  n is prime and else it is not prime

Example : 

Input : 11
Output : 11 is a prime number
Explanation : (11-1)! + 1 = 3628801
                       3628801 % 11 = 0 

               

Input : 8
Output : 8 is not prime number
Explanation : (8-1)! + 1 = 5041
                       5041 % 8 = 1 

Implementation of the above approach : 

C




// C program to check whether number is prime or not
#include <stdio.h>
  
int main()
{
    // code
    int n = 11;
    int m = n - 1;
    int factm = 1;
   // find factorial of n-1
    for (int i = 1; i <= m; i++) {
        factm *= i;
    }
  
  // add 1 to (n-1)!
    int factn = factm + 1;
    if (factn % n == 0) {
        // if remainder is 0 
        printf(" %d  is prime number",n);
    }
    else {
        printf("%d  is not prime number",n);
    }
    return 0;
}
// this code is contributed by devendra solunke

Output

 11  is prime number

Time Complexity: O(N) complexity only for calculating factorial  of (n-1) checking it is 0 or 1 using % takes constant time
Auxiliary Space: O(1)


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