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/*************************************************
How common are primes?

Write a program that reads a number n from the
user and returns the percentage of the first n
integers that are prime (we'll say 1 is *not*
prime).  Write and use a predicate isprime(k)
in your program.  Remember, a number k is prime
if 1 and k are the only numbers that evenly
divide k.
*************************************************/
#include <stdio.h>

int isprime(int p);

int main() {
  // Get value n
  int n;
  printf("Enter n: ");
  fflush(stdout);
  scanf(" %d", &n);

  // Count number of primes
  int count = 0;
  for(int k = 1; k <= n; k++) {
    if (isprime(k)) {
      count++;
    }
  }

  // Compute and print out percentage
  double p = count/(double)n * 100.0;
  printf("%g%% of the first %i integers are prime\n",
         count/(double)n * 100.0,
         n);

  return 0;
}

/***********************************
 ** isprime(k)
 ***********************************/
int isprime(int p) {
  // the smallest prime is 2
  if (p < 2) {
    return 0;
  }

  // search for divisors in [2,p-1]
  for(int div = 2; div < p; div++) {
    if (p % div == 0) {
      return 0;
    }
  }

  // no divisors were found, p's prime!
  return 1;
}