# C Program to Check Whether a Number is Prime or not

• Difficulty Level : Easy
• Last Updated : 17 Oct, 2022

Given a positive integer N. The task is to write a C program to check if the number is prime or not

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 ``#include ``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 `` ` `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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