Given a number n, the task is to calculate its primorial. 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 = 5Output:30 Priomorial = 2 * 3 * 5 = 30 As a side note, factorial is 2 * 3 * 4 * 5Input:n = 12Output: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) { int result = 1; // Initialize result // Multiply all primes up-to n and store in result for (int i = 0; primes[i] <= n ; i++) result = result * primes[i]; return result; } // Driver code int main() { int n = 15; 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 1 Primorial(P#) of 2 is 2 Primorial(P#) of 3 is 6 Primorial(P#) of 4 is 6 Primorial(P#) of 5 is 30 Primorial(P#) of 6 is 30 Primorial(P#) of 7 is 210 Primorial(P#) of 8 is 210 Primorial(P#) of 9 is 210 Primorial(P#) of 10 is 210 Primorial(P#) of 11 is 2310 Primorial(P#) of 12 is 2310 Primorial(P#) of 13 is 30030 Primorial(P#) of 14 is 30030 Primorial(P#) of 15 is 30030

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