C++ Program to check Prime Number

Given a positive integer, check if the number is prime or not. A prime is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples of first few prime numbers are {2, 3, 5,

Examples:

Input:  n = 11
Output: true

Input:  n = 15
Output: false

Input:  n = 1
Output: false

// A school method based C++ program to check if a 
// number is prime 
#include <bits/stdc++.h> 
using namespace std; 
  
bool isPrime(int n) 
{ 
    // Corner case 
    if (n <= 1) 
        return false; 
  
    // Check from 2 to n-1 
    for (int i = 2; i < n; i++) 
        if (n % i == 0) 
            return false; 
  
    return true; 
} 
  
// Driver Program to test above function 
int main() 
{ 
    isPrime(11) ? cout << " true\n" : cout << " false\n"; 
    isPrime(15) ? cout << " true\n" : cout << " false\n"; 
    return 0; 
} 

Output:

true
 false

Time complexity of this solution is O(n)

Optimized School Method

// A optimized school method based C++ program to check 
// if a number is prime 
#include <bits/stdc++.h> 
using namespace std; 
  
bool isPrime(int n) 
{ 
    // Corner cases 
    if (n <= 1) 
        return false; 
    if (n <= 3) 
        return true; 
  
    // This is checked so that we can skip 
    // middle five numbers in below loop 
    if (n % 2 == 0 || n % 3 == 0) 
        return false; 
  
    for (int i = 5; i * i <= n; i = i + 6) 
        if (n % i == 0 || n % (i + 2) == 0) 
            return false; 
  
    return true; 
} 
  
// Driver Program to test above function 
int main() 
{ 
    isPrime(11) ? cout << " true\n" : cout << " false\n"; 
    isPrime(15) ? cout << " true\n" : cout << " false\n"; 
    return 0; 
} 

Output:

true
 false

Please refer complete article on Primality Test | Set 1 (Introduction and School Method) for more details!

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