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# C++ Program To Check Whether a Number is Prime or not

• 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 using namespace std;    int main() {     int n, i, flag = 1;        // Ask user for input     cout << "Enter a number: ";        // Store input number in a variable     cin >> 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) {         cout << n << " is a prime number";     }     else {         cout << n << " is not a prime number";     }        return 0; }    // This code is contributed by shivanisinghss2110.

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 using namespace std;    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         cout << n << " is prime number";     }     else {         cout << n << " is not prime";     }     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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