# Find product of prime numbers between 1 to n

• Last Updated : 17 May, 2021

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 ``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

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## Javascript

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Output:

`210`

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