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

 2 years ago
source link: https://www.geeksforgeeks.org/find-third-number-such-that-sum-of-all-three-number-becomes-prime/
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Find third number such that sum of all three number becomes prime

  • Last Updated : 18 Mar, 2021

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: 2 
Explaination: 
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: 3 

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 untill it is less than a prime value.

Below is the implementation of the above approach: 

  • Python3
  • Javascript
// 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;
}
Output: 
3

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