# Find third number such that sum of all three number becomes prime

Given two numbers **A** and **B**. The task is to find the smallest positive integer greater than or equal to 1 such that the sum of all three numbers become a prime number.**Examples:**

Input:A = 2, B = 3Output:2Explanation:

The third number is 2 because if we add all three number the

sum obtained is 7 which is a prime number.Input:A = 5, B = 3Output:3

**Approach: **

- First of all store the sum of given 2 number in
**sum**variable. - Now, check if
**bitwise and (&)**of sum and 1 is equal to 1 or not (checking if the number is odd or not). - If it is equal to 1 then assign 2 to variable
**temp**and go to step 4. - Else check sum value of sum and temp variable whether it is prime number or not. If prime, then print the value of temp variable else add 2 to temp variable until it is less than a prime value.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function that will check` `// whether number is prime or not` `bool` `prime(` `int` `n)` `{` ` ` `for` `(` `int` `i = 2; i * i <= n; i++) {` ` ` `if` `(n % i == 0)` ` ` `return` `false` `;` ` ` `}` ` ` `return` `true` `;` `}` `// Function to print the 3rd number` `void` `thirdNumber(` `int` `a, ` `int` `b)` `{` ` ` `int` `sum = 0, temp = 0;` ` ` `sum = a + b;` ` ` `temp = 1;` ` ` `// If the sum is odd` ` ` `if` `(sum & 1) {` ` ` `temp = 2;` ` ` `}` ` ` `// If sum is not prime` ` ` `while` `(!prime(sum + temp)) {` ` ` `temp += 2;` ` ` `}` ` ` `cout << temp;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a = 3, b = 5;` ` ` `thirdNumber(a, b);` ` ` `return` `0;` `}` |

## Java

`// Java implementation of the approach` `import` `java.util.*;` ` ` `class` `GFG` `{` ` ` `// Function that will check` `// whether number is prime or not` `static` `boolean` `prime(` `int` `n)` `{` ` ` `for` `(` `int` `i = ` `2` `; i * i <= n; i++)` ` ` `{` ` ` `if` `(n % i == ` `0` `)` ` ` `return` `false` `;` ` ` `}` ` ` `return` `true` `;` `}` `// Function to print the 3rd number` `static` `void` `thirdNumber(` `int` `a, ` `int` `b)` `{` ` ` `int` `sum = ` `0` `, temp = ` `0` `;` ` ` `sum = a + b;` ` ` `temp = ` `1` `;` ` ` `// If the sum is odd` ` ` `if` `(sum == ` `0` `)` ` ` `{` ` ` `temp = ` `2` `;` ` ` `}` ` ` `// If sum is not prime` ` ` `while` `(!prime(sum + temp))` ` ` `{` ` ` `temp += ` `2` `;` ` ` `}` ` ` `System.out.print(temp);` `}` `// Driver code` `static` `public` `void` `main (String []arr)` `{` ` ` `int` `a = ` `3` `, b = ` `5` `;` ` ` ` ` `thirdNumber(a, b);` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 implementation of the above approach` `# Function that will check` `# whether number is prime or not` `def` `prime(n):` ` ` `for` `i ` `in` `range` `(` `2` `, n ` `+` `1` `):` ` ` `if` `i ` `*` `i > n ` `+` `1` `:` ` ` `break` ` ` `if` `(n ` `%` `i ` `=` `=` `0` `):` ` ` `return` `False` ` ` `return` `True` `# Function to print the 3rd number` `def` `thirdNumber(a, b):` ` ` `summ ` `=` `0` ` ` `temp ` `=` `0` ` ` `summ ` `=` `a ` `+` `b` ` ` `temp ` `=` `1` ` ` `#If the summ is odd` ` ` `if` `(summ & ` `1` `):` ` ` `temp ` `=` `2` ` ` `#If summ is not prime` ` ` `while` `(prime(summ ` `+` `temp) ` `=` `=` `False` `):` ` ` `temp ` `+` `=` `2` ` ` `print` `(temp)` `# Driver code` `a ` `=` `3` `b ` `=` `5` `thirdNumber(a, b)` `# This code is contributed by Mohit Kumar` |

## C#

`// C# implementation of the above approach` `using` `System;` `class` `GFG` `{` ` ` `// Function that will check` `// whether number is prime or not` `static` `bool` `prime(` `int` `n)` `{` ` ` `for` `(` `int` `i = 2; i * i <= n; i++)` ` ` `{` ` ` `if` `(n % i == 0)` ` ` `return` `false` `;` ` ` `}` ` ` `return` `true` `;` `}` `// Function to print the 3rd number` `static` `void` `thirdNumber(` `int` `a, ` `int` `b)` `{` ` ` `int` `sum = 0, temp = 0;` ` ` `sum = a + b;` ` ` `temp = 1;` ` ` `// If the sum is odd` ` ` `if` `(sum == 0)` ` ` `{` ` ` `temp = 2;` ` ` `}` ` ` `// If sum is not prime` ` ` `while` `(!prime(sum + temp))` ` ` `{` ` ` `temp += 2;` ` ` `}` ` ` `Console.Write (temp);` `}` `// Driver code` `static` `public` `void` `Main ()` `{` ` ` `int` `a = 3, b = 5;` ` ` ` ` `thirdNumber(a, b);` `}` `}` `// This code is contributed by Sachin.` |

## Javascript

`<script>` ` ` `// Javascript implementation of the above approach` ` ` ` ` `// Function that will check` ` ` `// whether number is prime or not` ` ` `function` `prime(n)` ` ` `{` ` ` `for` `(let i = 2; i * i <= n; i++) {` ` ` `if` `(n % i == 0)` ` ` `return` `false` `;` ` ` `}` ` ` `return` `true` `;` ` ` `}` ` ` `// Function to print the 3rd number` ` ` `function` `thirdNumber(a, b)` ` ` `{` ` ` `let sum = 0, temp = 0;` ` ` `sum = a + b;` ` ` `temp = 1;` ` ` `// If the sum is odd` ` ` `if` `((sum & 1) != 0) {` ` ` `temp = 2;` ` ` `}` ` ` `// If sum is not prime` ` ` `while` `(!prime(sum + temp)) {` ` ` `temp += 2;` ` ` `}` ` ` `document.write(temp);` ` ` `}` ` ` ` ` `let a = 3, b = 5;` ` ` `thirdNumber(a, b);` `// This code is contributed by divyeshrabadiya07.` `</script>` |

**Output:**

3

Time Complexity: O(sqrt(n))

Auxiliary Space: O(1)