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# 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 = 3
Output:
Explanation:
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 = 3
Output:

Approach:

1. First of all store the sum of given 2 number in sum variable.
2. Now, check if bitwise and (&) of sum and 1 is equal to 1 or not (checking if the number is odd or not).
3. If it is equal to 1 then assign 2 to variable temp and go to step 4.
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 ``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

 ``

Output:

`3`

Time Complexity: O(sqrt(n))

Auxiliary Space: O(1)

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