# Find two distinct prime numbers with given product

• Difficulty Level : Easy
• Last Updated : 26 May, 2022

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++

 `// C++ program to find a distinct prime number``// pair whose product is equal to given number``#include ``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;``}`

## C

 `// C program to find a distinct prime number``// pair whose product is equal to given number``#include ``#include ` `// 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] && x != i && x * i == n) {``            ``printf``(``"%d %d"``,i,x);``            ``flag = 1;``            ``return``;``        ``}``    ``}` `    ``if` `(!flag)``        ``printf``(``"No such pair found"``);``}` `// Driven Code``int` `main()``{``    ``int` `n = 39;` `    ``findPrimePair(n);` `    ``return` `0;``}` `// This code is contributed by kothavvsaakash.`

## Java

 `// 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`

## Python3

 `# 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`

## C#

 `// 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`

## PHP

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## Javascript

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Output:

`3 13`

Time Complexity: O(N*log log(N))

Auxiliary Space: O(N)

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