// program that prints all the Euclid numbers until the first composite
// Euclid number is reached.The program implements the following two
// functions (other than the main):
// 	1. int isprime(int n): returns 1 if n is prime, 0 otherwise
//      2. int primorial(int n): returns the primorial of n
//         
// Author:rahule@cse.iitk.ac.in
// 

#include<stdio.h>
int isprime(int);    // returns 1 if n is prime, 0 otherwise
int primorial(int);  // returns the primorial of n
main()
{
  int i,e;
  for(i=1;;i++)		//Runs till a composite Euclid number is found.the "condition" of "for loop" is left blank,since we are not checking for a condition.
                        //the loop breaks once a composite Euclid number is found
  {
    e=primorial(i)+1;	//calculates ith Euclid numer
    if(!isprime(e))	//checks whether it is NOT prime.If NOT prime,breaks.
      break;
    else		//if it is prime,prints it
      printf("the %dth Euclid number is:  %d\n",i,e);
  }
  printf("\nthe %dth Euclid number %d is composite!  exiting..\n",i,e);		//prints the first Euclid number which is a composite number
}

int primorial(int n)
// returns the primorial of n
{
  int cnt=0,i=2,p=1;
  if(n==0)		//base case.p(0)=1
    return(1);
  while(cnt<n)		//till n prime numbers are multiplied,do this loop
  {
    if(isprime(i))	//if an i is found to be prime,multiply it and increament the count
    {
      p=p*i;
      cnt++;
    }
    i++;		//increament the value of i
  }
  return(p);		//return the calculated value of p
}

int isprime(int n) 
// returns 1 if n is prime, 0 otherwise
{
  int i;
  if(n==2)	//base condition.2 is prime
    return(1);
  for(i=2;i<=n/2;i++)
  {
    if(n%i==0)		//if n has a factor,then return 0;NOT prime
      return(0);
  }
  return(1);		//if the loop happens to complete,then there are no factors for n,hence it is prime.Return 1
}