Find product of prime numbers between 1 to n

Given a number n, we need to find the product of all prime numbers between 1 to n.
Examples:

Input: 5
Output: 30
Explanation: product of prime numbers between 1 to 5 is 2 * 3 * 5 = 30 

Input : 7
Output : 210

Using Sieve of Eratosthenes to find all prime numbers from 1 to n then compute the product.

Following is the algorithm to find all the prime numbers less than or equal to a given integer n by Eratosthenes’ method: 
When the algorithm terminates, all the numbers in the list that are not marked are prime and using a loop we compute the product of prime numbers. 

C++

// CPP Program to find product
// of prime numbers between 1 to n
#include <bits/stdc++.h>
using namespace std;

// Returns product of primes in range from
// 1 to n.
long ProdOfPrimes(int n)
{
    // Array to store prime numbers
    bool prime[n + 1];

    // Create a boolean array "prime[0..n]"
    // and initialize all entries it as true.
    // A value in prime[i] will finally be
    // false if i is Not a prime, else true.
    memset(prime, true, n + 1);

    for (int p = 2; p * p <= n; p++) {

        // If prime[p] is not changed, then
        // it is a prime
        if (prime[p] == true) {

            // Update all multiples of p
            for (int i = p * 2; i <= n; i += p)
                prime[i] = false;
        }
    }

    // Return product of primes generated
    // through Sieve.
    long prod = 1;
    for (int i = 2; i <= n; i++)
        if (prime[i])
            prod *= i;
    return prod;
}

// Driver code
int main()
{
    int n = 10;
    cout << ProdOfPrimes(n);
    return 0;
}

Java

// Java Program to find product
// of prime numbers between 1 to n
import java.util.Arrays;

class GFG {

    // Returns product of primes in range from
    // 1 to n.
    static long ProdOfPrimes(int n)
    {

        // Array to store prime numbers
        boolean prime[]=new boolean[n + 1];

        // Create a boolean array "prime[0..n]"
        // and initialize all entries it as true.
        // A value in prime[i] will finally be
        // false if i is Not a prime, else true.
        Arrays.fill(prime, true);

        for (int p = 2; p * p <= n; p++) {

            // If prime[p] is not changed, then
            // it is a prime
            if (prime[p] == true) {

                // Update all multiples of p
                for (int i = p * 2; i <= n; i += p)
                    prime[i] = false;
            }
        }

        // Return product of primes generated
        // through Sieve.
        long prod = 1;

        for (int i = 2; i <= n; i++)
            if (prime[i])
                prod *= i;

        return prod;
    }

    // Driver code
    public static void main (String[] args)
    {

        int n = 10;

        System.out.print(ProdOfPrimes(n));
    }
}

// This code is contributed by Anant Agarwal.

Python3

# Python3 Program to find product
# of prime numbers between 1 to n

# Returns product of primes
# in range from 1 to n.
def ProdOfPrimes(n):

    # Array to store prime numbers
    prime = [True for i in range(n + 1)]

    # Create a boolean array "prime[0..n]"
    # and initialize all entries it as true.
    # A value in prime[i] will finally be
    # false if i is Not a prime, else true.
    p = 2
    while(p * p <= n):

        # If prime[p] is not changed,
        # then it is a prime
        if (prime[p] == True):

            # Update all multiples of p
            i = p * 2
            while(i <= n):
                prime[i] = False
                i += p
        p += 1

    # Return product of primes
    # generated through Sieve.
    prod = 1
    for i in range(2, n+1):
        if (prime[i]):
            prod *= i
    return prod

# Driver code
n = 10
print(ProdOfPrimes(n))

# This code is contributed by Anant Agarwal.

C#

// C# Program to find product of
// prime numbers between 1 to n
using System;

public class GFG
{

    // Returns product of primes
    // in range from 1 to n.
    static long ProdOfPrimes(int n)
    {

        // Array to store prime numbers
        bool []prime=new bool[n + 1];

        // Create a boolean array "prime[0..n]"
        // and initialize all entries it as true.
        // A value in prime[i] will finally be
        // false if i is Not a prime, else true.
        for(int i = 0; i < n + 1; i++)
            prime[i] = true;

        for (int p = 2; p * p <= n; p++) {

            // If prime[p] is not changed,
            // then it is a prime
            if (prime[p] == true) {

                // Update all multiples of p
                for (int i = p * 2; i <= n; i += p)
                    prime[i] = false;
            }
        }

        // Return product of primes generated
        // through Sieve.
        long prod = 1;

        for (int i = 2; i <= n; i++)
            if (prime[i])
                prod *= i;

        return prod;
    }

    // Driver code
    public static void Main ()
    {

        int n = 10;

        Console.Write(ProdOfPrimes(n));
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP Program to find product
// of prime numbers between 1 to n

// Returns product of primes
// in range from 1 to n.
function ProdOfPrimes($n)
{
    // Array to store prime
    // numbers Create a boolean
    // array "prime[0..n]" and
    // initialize all entries it
    // as true. A value in prime[i]
    // will finally be false if i
    // is Not a prime, else true.
    $prime = array();
    for($i = 0; $i < $n + 1; $i++)
        $prime[$i] = true;

    for ($p = 2; $p * $p <= $n; $p++)
    {

        // If prime[p] is not changed,
        // then it is a prime
        if ($prime[$p] == true)
        {

            // Update all multiples of p
            for ($i = $p * 2; $i <= $n;
                              $i += $p)
                $prime[$i] = false;
        }
    }

    // Return product of primes
    // generated through Sieve.
    $prod = 1;
    for ($i = 2; $i <= $n; $i++)
        if ($prime[$i])
            $prod *= $i;
    return $prod;
}

// Driver Code
$n = 10;
echo (ProdOfPrimes($n));

// This code is contributed by
// Manish Shaw(manishshaw1)
?>

Javascript

<script>
    // Javascript Program to find product of
    // prime numbers between 1 to n

    // Returns product of primes
    // in range from 1 to n.
    function ProdOfPrimes(n)
    {

        // Array to store prime numbers
        let prime = new Array(n + 1);
        prime.fill(0);

        // Create a boolean array "prime[0..n]"
        // and initialize all entries it as true.
        // A value in prime[i] will finally be
        // false if i is Not a prime, else true.
        for(let i = 0; i < n + 1; i++)
            prime[i] = true;

        for (let p = 2; p * p <= n; p++) {

            // If prime[p] is not changed,
            // then it is a prime
            if (prime[p] == true) {

                // Update all multiples of p
                for (let i = p * 2; i <= n; i += p)
                    prime[i] = false;
            }
        }

        // Return product of primes generated
        // through Sieve.
        let prod = 1;

        for (let i = 2; i <= n; i++)
            if (prime[i])
                prod *= i;

        return prod;
    }

    let n = 10;

      document.write(ProdOfPrimes(n));

</script>

Output:

210

Time Complexity: O(n log log n) // for sieve of erastosthenes

Auxiliary Space: O(N) //an extra array is used to store all the prime numbers hence algorithm takes up linear space