# Program to find the next prime number

Given an integer N. The task is to find the next prime number i.e. the smallest prime number greater than N.

Examples:

Input: N = 10
Output: 11
11 is the smallest prime number greater than 10.

Input: N = 0
Output: 2

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. First of all, take a boolean variable found and initialise it to false.
2. Now, until that variable not equals to true, increment N by 1 in each iteration and check whether it is prime or not.
3. If it is prime then print it and change value of found variable to True. otherwise, iterate the loop untill you will get the next prime number.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function that returns true if n  ` `// is prime else returns false  ` `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``;  ` `}  ` ` `  `// Function to return the smallest ` `// prime number greater than N ` `int` `nextPrime(``int` `N) ` `{ ` ` `  `    ``// Base case ` `    ``if` `(N <= 1) ` `        ``return` `2; ` ` `  `    ``int` `prime = N; ` `    ``bool` `found = ``false``; ` ` `  `    ``// Loop continuously until isPrime returns ` `    ``// true for a number greater than n ` `    ``while` `(!found) { ` `        ``prime++; ` ` `  `        ``if` `(isPrime(prime)) ` `            ``found = ``true``; ` `    ``} ` ` `  `    ``return` `prime; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `N = 3; ` ` `  `    ``cout << nextPrime(N); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach  ` `class` `GFG  ` `{ ` ` `  `    ``// Function that returns true if n  ` `    ``// is prime else returns false  ` `    ``static` `boolean` `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``;  ` `    ``}  ` `     `  `    ``// Function to return the smallest  ` `    ``// prime number greater than N  ` `    ``static` `int` `nextPrime(``int` `N)  ` `    ``{  ` `     `  `        ``// Base case  ` `        ``if` `(N <= ``1``)  ` `            ``return` `2``;  ` `     `  `        ``int` `prime = N;  ` `        ``boolean` `found = ``false``;  ` `     `  `        ``// Loop continuously until isPrime returns  ` `        ``// true for a number greater than n  ` `        ``while` `(!found)  ` `        ``{  ` `            ``prime++;  ` `     `  `            ``if` `(isPrime(prime))  ` `                ``found = ``true``;  ` `        ``}  ` `     `  `        ``return` `prime;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `main (String[] args) ` `    ``{  ` `        ``int` `N = ``3``;  ` `     `  `        ``System.out.println(nextPrime(N));  ` `    ``}  ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach  ` `import` `math ` ` `  `# Function that returns True if n  ` `# is prime else returns False  ` `def` `isPrime(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` `or` `n ``%` `3` `=``=` `0``): ` `        ``return` `False` `     `  `    ``for` `i ``in` `range``(``5``,``int``(math.sqrt(n) ``+` `1``), ``6``):  ` `        ``if``(n ``%` `i ``=``=` `0` `or` `n ``%` `(i ``+` `2``) ``=``=` `0``): ` `            ``return` `False` `     `  `    ``return` `True` ` `  `# Function to return the smallest  ` `# prime number greater than N  ` `def` `nextPrime(N): ` ` `  `    ``# Base case  ` `    ``if` `(N <``=` `1``): ` `        ``return` `2` ` `  `    ``prime ``=` `N ` `    ``found ``=` `False` ` `  `    ``# Loop continuously until isPrime returns  ` `    ``# True for a number greater than n  ` `    ``while``(``not` `found): ` `        ``prime ``=` `prime ``+` `1` ` `  `        ``if``(isPrime(prime) ``=``=` `True``): ` `            ``found ``=` `True` ` `  `    ``return` `prime ` ` `  `# Driver code  ` `N ``=` `3` `print``(nextPrime(N)) ` ` `  `# This code is contributed by Sanjit_Prasad `

## C#

 `// C# implementation of the approach  ` `using` `System; ` `     `  `class` `GFG  ` `{ ` ` `  `    ``// Function that returns true if n  ` `    ``// is prime else returns false  ` `    ``static` `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``;  ` `    ``}  ` `     `  `    ``// Function to return the smallest  ` `    ``// prime number greater than N  ` `    ``static` `int` `nextPrime(``int` `N)  ` `    ``{  ` `     `  `        ``// Base case  ` `        ``if` `(N <= 1)  ` `            ``return` `2;  ` `     `  `        ``int` `prime = N;  ` `        ``bool` `found = ``false``;  ` `     `  `        ``// Loop continuously until isPrime  ` `        ``// returns true for a number  ` `        ``// greater than n  ` `        ``while` `(!found)  ` `        ``{  ` `            ``prime++;  ` `     `  `            ``if` `(isPrime(prime))  ` `                ``found = ``true``;  ` `        ``}  ` `        ``return` `prime;  ` `    ``}  ` `     `  `    ``// Driver code  ` `    ``public` `static` `void` `Main (String[] args) ` `    ``{  ` `        ``int` `N = 3;  ` `     `  `        ``Console.WriteLine(nextPrime(N));  ` `    ``}  ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:

```5
```

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