Given a number n, the task is to calculate its primorial. Primorial (denoted as P_{n}#) is product of first n prime numbers. Primorial of a number is similar to factorial of a number. In primorial, not all the natural numbers get multiplied only prime numbers are multiplied to calculate the primorial of a number. It is denoted with P#.

Examples:

Input:n = 3Output:30 Priomorial = 2 * 3 * 5 = 30 As a side note, factorial is 2 * 3 * 4 * 5Input:n = 5Output:2310 Primorial = 2 * 3 * 5 * 7 * 11

A ** naive approach ** is to check all numbers from 1 to n one by one is prime or not, if yes then store the multiplication in result, similarly store the result of multiplication of primes till n.

An ** efficient ** method is to find all the prime up-to n using Sieve of Sundaram and then just calculate the primorial by multiplying them all.

`// C++ program to find Primorial of given numbers ` `#include<bits/stdc++.h> ` `using` `namespace` `std; ` `const` `int` `MAX = 1000000; ` ` ` `// vector to store all prime less than and equal to 10^6 ` `vector <` `int` `> primes; ` ` ` `// Function for sieve of sundaram. This function stores all ` `// prime numbers less than MAX in primes ` `void` `sieveSundaram() ` `{ ` ` ` `// In general Sieve of Sundaram, produces primes smaller ` ` ` `// than (2*x + 2) for a number given number x. Since ` ` ` `// we want primes smaller than MAX, we reduce MAX to half ` ` ` `// This array is used to separate numbers of the form ` ` ` `// i+j+2ij from others where 1 <= i <= j ` ` ` `bool` `marked[MAX/2 + 1] = {0}; ` ` ` ` ` `// Main logic of Sundaram. Mark all numbers which ` ` ` `// do not generate prime number by doing 2*i+1 ` ` ` `for` `(` `int` `i = 1; i <= (` `sqrt` `(MAX)-1)/2 ; i++) ` ` ` `for` `(` `int` `j = (i*(i+1))<<1 ; j <= MAX/2 ; j += 2*i +1) ` ` ` `marked[j] = ` `true` `; ` ` ` ` ` `// Since 2 is a prime number ` ` ` `primes.push_back(2); ` ` ` ` ` `// Print other primes. Remaining primes are of the ` ` ` `// form 2*i + 1 such that marked[i] is false. ` ` ` `for` `(` `int` `i=1; i<=MAX/2; i++) ` ` ` `if` `(marked[i] == ` `false` `) ` ` ` `primes.push_back(2*i + 1); ` `} ` ` ` `// Function to calculate primorial of n ` `int` `calculatePrimorial(` `int` `n) ` `{ ` ` ` `// Multiply first n primes ` ` ` `int` `result = 1; ` ` ` `for` `(` `int` `i=0; i<n; i++) ` ` ` `result = result * primes[i]; ` ` ` `return` `result; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 5; ` ` ` `sieveSundaram(); ` ` ` `for` `(` `int` `i = 1 ; i<= n; i++) ` ` ` `cout << ` `"Primorial(P#) of "` `<< i << ` `" is "` ` ` `<< calculatePrimorial(i) <<endl; ` ` ` `return` `0; ` `} ` |

Output:

Primorial(P#) of 1 is 2 Primorial(P#) of 2 is 6 Primorial(P#) of 3 is 30 Primorial(P#) of 4 is 210 Primorial(P#) of 5 is 2310

This article is contributed by **Sahil Chhabra (KILLER)**. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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