Find two prime numbers with given sum

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++ 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 sum
void 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 program
int main()
{
    int n = 74;
    findPrimePair(n);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

C

// 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 sum
void 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 program
int main()
{
    int n = 74;
    findPrimePair(n);
    return 0;
}

// This code is contributed by Aditya Kumar (adityakumar129)

Java

// 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

# 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 sum
def 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 program
n = 74
findPrimePair(n)

# This code is contributed by
# Smitha Dinesh Semwal

C#

// 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
// 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 sum
function 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
?>

Javascript

<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

Time complexity: O(n*log(logn))

Auxiliary Space: O(n)

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