Find two prime numbers with given sum

Last Updated : 21 Sep, 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++ 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)

Suggest improvement

Find the smallest twins in given range

Find all distinct subset (or subsequence) sums of an array

Share your thoughts in the comments

Find two prime numbers with given sum

C++

C

Java

Python 3

C#

PHP

Javascript

Please Login to comment...

Similar Reads

What kind of Experience do you want to share?