# 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 ` `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 ` `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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