Find two distinct prime numbers with given product

Given a number N (greater than 2 ). The task is to find two distinct prime numbers whose product will be equal to the given number. There may be several combinations possible. Print only first such pair.

If it is not possible to express N as a product of two distinct primes, print “Not Possible”.

Examples:



Input : N = 15
Output : 3, 5
3 and 5 are both primes and,
3*5 = 15

Input : N = 39
Output : 3, 13
3 and 13 are both primes and,
3*13 = 39

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 a pair with a given product.

Below is the implementation of the above approach:

C++

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// C++ program to find a distinct prime number
// pair whose product is equal to given number
#include <bits/stdc++.h>
using namespace std;
  
// Function to 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 * 2; i <= n; i += p)
                isPrime[i] = false;
        }
    }
}
  
// Function to print a prime pair
// with given product
void findPrimePair(int n)
{
    int flag = 0;
  
    // Generating primes using Sieve
    bool isPrime[n + 1];
    SieveOfEratosthenes(n, isPrime);
  
    // Traversing all numbers to find first
    // pair
    for (int i = 2; i < n; i++) {
        int x = n / i;
  
        if (isPrime[i] && isPrime[x] and x != i and x * i == n) {
            cout << i << " " << x;
            flag = 1;
            return;
        }
    }
  
    if (!flag)
        cout << "No such pair found";
}
  
// Driven Code
int main()
{
    int n = 39;
  
    findPrimePair(n);
  
    return 0;
}

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Java

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// Java program to find a distinct prime number
// pair whose product is equal to given number
  
  
class GFG
{
              
        // Function to generate all prime
        // numbers less than n
          
        static void 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 * 2; i <= n; i += p)
                        isPrime[i] = false;
                }
            }
        }
          
        // Function to print a prime pair
        // with given product
        static void findPrimePair(int n)
        {
            int flag = 0;
          
            // Generating primes using Sieve
            boolean []isPrime= new boolean[n + 1];
            SieveOfEratosthenes(n, isPrime);
          
            // Traversing all numbers to find first
            // pair
            for (int i = 2; i < n; i++) {
                int x = n / i;
          
                if (isPrime[i] && isPrime[x] && x != i && x * i == n)
                {
                    System.out.println(i + " " + x);
                    flag = 1;
                    return;
                }
            }
          
            if (flag==0)
                System.out.println("No such pair found");
        }
          
        // Driven Code
        public static void main(String [] args)
        {
            int n = 39;
          
            findPrimePair(n);
          
        }
  
}
  
// This code is contributed by
// ihritik

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Python 3

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# Python3 program to find a distinct 
# prime number pair whose product
# is equal to given number 
  
# from math lib. import everything
from math import *
  
# Function to 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, False
  
    for i in range(2, n + 1) :
        isPrime[i] = True
  
    for p in range(2, int(sqrt(n)) + 1) :
  
        # If isPrime[p] is not changed, 
        # then it is a prime 
        if isPrime[p] == True :
  
            for i in range(p * 2, n + 1, p) :
                isPrime[i] = False
  
# Function to print a prime pair 
# with given product 
def findPrimePair(n) :
  
    flag = 0
      
    # Generating primes using Sieve 
    isPrime = [False] * (n + 1)
    SieveOfEratosthenes(n, isPrime)
  
    # Traversing all numbers to 
    # find first pair
    for i in range(2, n) :
        x = int(n / i)
  
        if (isPrime[i] & isPrime[x] and 
             x != i and x * i == n) :
            print(i, x)
            flag = 1
            break
  
    if not flag :
        print("No such pair found")
      
# Driver code     
if __name__ == "__main__" :
  
    # Function calling
    n = 39
  
    findPrimePair(n)
  
# This code is contributed by ANKITRAI1

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C#

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// C# program to find a distinct prime number
// pair whose product is equal to given number
using System; 
class GFG
{
      
// Function to generate all 
// prime numbers less than n
static void SieveOfEratosthenes(int n, 
                                bool[] isPrime)
{
    // Initialize all entries of bool 
    // 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 * 2; i <= n; i += p)
                isPrime[i] = false;
        }
    }
}
  
// Function to print a prime 
// pair with given product
static void findPrimePair(int n)
{
    int flag = 0;
  
    // Generating primes using Sieve
    bool[] isPrime = new bool[n + 1];
    SieveOfEratosthenes(n, isPrime);
  
    // Traversing all numbers to 
    // find first pair
    for (int i = 2; i < n; i++)
    {
        int x = n / i;
  
        if (isPrime[i] && isPrime[x] && 
                x != i && x * i == n)
        {
            Console.Write(i + " " + x);
            flag = 1;
            return;
        }
    }
  
    if (flag == 0)
        Console.Write("No such pair found");
}
  
// Driven Code
public static void Main()
{
    int n = 39;
  
    findPrimePair(n);
}
}
  
// This code is contributed by ChitraNayal

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PHP

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<?php
// PHP program to find a distinct prime number
// pair whose product is equal to given number
  
// Function to 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] = false;
    $isPrime[1] = false;
    for ($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[$p])
        {
            // Update all multiples of p
            for ($i = $p * 2; 
                 $i <= $n; $i += $p)
                $isPrime[$i] = false;
        }
    }
}
  
// Function to print a prime pair
// with given product
function findPrimePair($n)
{
    $flag = 0;
  
    // Generating primes using Sieve
    $isPrime = array_fill(0, ($n + 1), false);
    SieveOfEratosthenes($n, $isPrime);
  
    // Traversing all numbers to 
    // find first pair
    for ($i = 2; $i < $n; $i++) 
    {
        $x = (int)($n / $i);
  
        if ($isPrime[$i] && $isPrime[$x] and
               $x != $i and $x * $i == $n)
        {
            echo $i . " " . $x;
            $flag = 1;
            return;
        }
    }
  
    if (!$flag)
        echo "No such pair found";
}
  
// Driver Code
$n = 39;
  
findPrimePair($n);
  
// This code is contributed by mits
?>

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Output:

3 13


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