Find two prime numbers with given sum

02 May, 2022
Given an even number (greater than 2 ), print two prime numbers whose sum will be equal to given number. There may be several combinations possible. Print only first such pair. An interesting point is, a solution always exist according to Goldbach’s conjecture.Examples :  
Input: n = 74
Output: 3 71

Input : n = 1024
Output: 3 1021

Input: n = 66
Output: 5 61

Input: n = 9990
Output: 17 9973
 
The idea is to find all the primes less than or equal to the given number N using Sieve of Eratosthenes. Once we have an array that tells all primes, we can traverse through this array to find pair with given sum.  
C++
C
Java
Python 3
C#
PHP
Javascript
// C++ program to find a prime number pair whose sum is// equal to given number// C++ program to print super primes less than or equal to n.#include <bits/stdc++.h>using namespace std; // Generate all prime numbers less than n.bool SieveOfEratosthenes(int n, bool isPrime[]){    // Initialize all entries of boolean array as true. A    // value in isPrime[i] will finally be false if i is Not    // a prime, else true bool isPrime[n+1];    isPrime[0] = isPrime[1] = false;    for (int i = 2; i <= n; i++)        isPrime[i] = true;     for (int p = 2; p * p <= n; p++) {        // If isPrime[p] is not changed, then it is a prime        if (isPrime[p] == true) {            // Update all multiples of p            for (int i = p * p; i <= n; i += p)                isPrime[i] = false;        }    }} // Prints a prime pair with given sumvoid findPrimePair(int n){    // Generating primes using Sieve    bool isPrime[n + 1];    SieveOfEratosthenes(n, isPrime);     // Traversing all numbers to find first pair    for (int i = 0; i < n; i++) {        if (isPrime[i] && isPrime[n - i]) {            cout << i << " " << (n - i);            return;        }    }} // Driven programint main(){    int n = 74;    findPrimePair(n);    return 0;} // This code is contributed by Aditya Kumar (adityakumar129)
// C program to find a prime number pair whose sum is// equal to given number// C program to print super primes less than or equal to n.#include <stdio.h>#include <stdbool.h> // Generate all prime numbers less than n.bool SieveOfEratosthenes(int n, bool isPrime[]){    // Initialize all entries of boolean array as true. A    // value in isPrime[i] will finally be false if i is Not    // a prime, else true bool isPrime[n+1];    isPrime[0] = isPrime[1] = false;    for (int i = 2; i <= n; i++)        isPrime[i] = true;     for (int p = 2; p * p <= n; p++) {        // If isPrime[p] is not changed, then it is a prime        if (isPrime[p] == true) {            // Update all multiples of p            for (int i = p * p; i <= n; i += p)                isPrime[i] = false;        }    }} // Prints a prime pair with given sumvoid findPrimePair(int n){    // Generating primes using Sieve    bool isPrime[n + 1];    SieveOfEratosthenes(n, isPrime);     // Traversing all numbers to find first    // pair    for (int i = 0; i < n; i++) {        if (isPrime[i] && isPrime[n - i]) {            printf("%d  %d",i,n-i);            return;        }    }} // Driven programint main(){    int n = 74;    findPrimePair(n);    return 0;} // This code is contributed by Aditya Kumar (adityakumar129)
// Java program to find a prime number pair whose sum is// equal to given number// Java program to print super primes less than or equal to n. class GFG {    // Generate all prime numbers less than n.    static boolean SieveOfEratosthenes(int n, boolean isPrime[])    {        // Initialize all entries of boolean array as true.        // A value in isPrime[i] will finally be false if i        // is Not a prime, else true bool isPrime[n+1];        isPrime[0] = isPrime[1] = false;        for (int i = 2; i <= n; i++)            isPrime[i] = true;         for (int p = 2; p * p <= n; p++) {            // If isPrime[p] is not changed, then it is a            // prime            if (isPrime[p] == true) {                // Update all multiples of p                for (int i = p * p; i <= n; i += p)                    isPrime[i] = false;            }        }        return false;    }     // Prints a prime pair with given sum    static void findPrimePair(int n)    {        // Generating primes using Sieve        boolean isPrime[] = new boolean[n + 1];        SieveOfEratosthenes(n, isPrime);         // Traversing all numbers to find first pair        for (int i = 0; i < n; i++) {            if (isPrime[i] && isPrime[n - i]) {                System.out.print(i + " " + (n - i));                return;            }        }    }     // Driver code    public static void main(String[] args)    {        int n = 74;        findPrimePair(n);    }} // This code is contributed by Aditya Kumar (adityakumar129)
# Python 3 program to find a prime number# pair whose sum is equal to given number# Python 3 program to print super primes# less than or equal to n. # Generate all prime numbers less than n.def SieveOfEratosthenes(n, isPrime):     # Initialize all entries of boolean    # array as True. A value in isPrime[i]    # will finally be False if i is Not a    # prime, else True bool isPrime[n+1]    isPrime[0] = isPrime[1] = False    for i in range(2, n+1):        isPrime[i] = True     p = 2    while(p*p <= n):             # If isPrime[p] is not changed,        # then it is a prime        if (isPrime[p] == True):                     # Update all multiples of p            i = p*p            while(i <= n):                isPrime[i] = False                i += p        p += 1         # Prints a prime pair with given sumdef findPrimePair(n):     # Generating primes using Sieve    isPrime = [0] * (n+1)    SieveOfEratosthenes(n, isPrime)     # Traversing all numbers to find    # first pair    for i in range(0, n):             if (isPrime[i] and isPrime[n - i]):                     print(i,(n - i))            return             # Driven programn = 74findPrimePair(n) # This code is contributed by# Smitha Dinesh Semwal
// C# program to find a prime number pair whose// sum is equal to given number// C# program to print super primes less than// or equal to n.using System; class GFG{    // Generate all prime numbers less than n.    static bool SieveOfEratosthenes(int n, bool []isPrime)    {        // Initialize all entries of boolean        // array as true. A value in isPrime[i]        // will finally be false if i is Not a        // prime, else true bool isPrime[n+1];        isPrime[0] = isPrime[1] = false;        for (int i = 2; i <= n; i++)            isPrime[i] = true;             for (int p = 2; p * p <= n; p++)        {            // If isPrime[p] is not changed,            // then it is a prime            if (isPrime[p] == true)            {                // Update all multiples of p                for (int i = p * p; i <= n; i += p)                    isPrime[i] = false;            }        }        return false;    }         // Prints a prime pair with given sum    static void findPrimePair(int n)    {        // Generating primes using Sieve        bool []isPrime=new bool[n + 1];        SieveOfEratosthenes(n, isPrime);             // Traversing all numbers to find first        // pair        for (int i = 0; i < n; i++)        {            if (isPrime[i] && isPrime[n - i])            {                Console.Write(i + " " + (n - i));                return;            }        }    }         // Driver code    public static void Main ()    {        int n = 74;        findPrimePair(n);    }} // This code is contributed by vt_m.
<?php// PHP program to find a prime// number pair whose sum is equal// to given number // Generate all prime numbers// less than n.function SieveOfEratosthenes($n, &$isPrime){    // Initialize all entries of    // boolean array as true. A value    // in isPrime[i] will finally    // be false if i is Not a prime,    // else true bool isPrime[n+1];    $isPrime[0] = $isPrime[1] = false;    for ($i = 2; $i <= $n; $i++)        $isPrime[$i] = true;     for ($p = 2; $p * $p <= $n; $p++)    {        // If isPrime[p] is not changed,        // then it is a prime        if ($isPrime[$p] == true)        {            // Update all multiples of p            for ($i = $p * $p;                 $i <= $n; $i += $p)                $isPrime[$i] = false;        }    }} // Prints a prime pair with given sumfunction findPrimePair($n){    // Generating primes using Sieve    $isPrime = array_fill(0, $n + 1, NULL);    SieveOfEratosthenes($n, $isPrime);     // Traversing all numbers    // to find first pair    for ($i = 0; $i < $n; $i++)    {        if ($isPrime[$i] &&            $isPrime[$n - $i])        {            echo $i . " " . ($n - $i);            return;        }    }} // Driver Code$n = 74;findPrimePair($n); // This code is contributed// by ChitraNayal?>
<script> // Javascript program to find a prime number pair whose// sum is equal to given number// Java program to print super primes less than// or equal to n.     // Generate all prime numbers less than n.    function SieveOfEratosthenes(n,isPrime)    {        // Initialize all entries of boolean        // array as true. A value in isPrime[i]        // will finally be false if i is Not a        // prime, else true bool isPrime[n+1];        isPrime[0] = isPrime[1] = false;        for (let i = 2; i <= n; i++)            isPrime[i] = true;               for (let p = 2; p * p <= n; p++)        {            // If isPrime[p] is not changed,            // then it is a prime            if (isPrime[p] == true)            {                // Update all multiples of p                for (let i = p * p; i <= n; i += p)                    isPrime[i] = false;            }        }        return false;    }         // Prints a prime pair with given sum    function findPrimePair(n)    {        // Generating primes using Sieve        let isPrime = new Array(n+1);        for(let i=0;i<n+1;i++)        {            isPrime[i]=false;        }        SieveOfEratosthenes(n, isPrime);               // Traversing all numbers to find first        // pair        for (let i = 0; i < n; i++)        {            if (isPrime[i] && isPrime[n - i])            {                document.write(i + " " + (n - i));                return;            }        }    }         // Driver code    let  n = 74;    findPrimePair(n);         // This code is contributed by rag2127     </script>
Output:  
3 71
This article is contributed by Rakesh Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
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