#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>

// pnut.c - lrb
// gcc pnut.c -lm -o pnut

/*
The Prime Number Theorem says that n divided by the number of primes
less than n approaches the natural logarithm of n. This program counts
the number of primes less than n and displays this ratio and the natural
logarithm of n.
*/

int isprime(int number) {
 if (number<=1) return 0;
 int i;
 for (i=2;i*i<=number;++i) {
  if (number%i==0) return 0;
  }
 return 1;
 }

void usage() {
 printf("\npnut.c - 2/3/20");
 printf("\n\nUsage: pnut -n number where n < 10000000\n");
 exit(1);
 }

int main(int argc,char *argv[]) {
 if (argc!=3) usage();
 unsigned int i,n,ctr=1;
 for (i=1;i<argc;++i) {
  if (strcmp(argv[i],"-n")==0) {++i;n=atoi(argv[i]);}
  else usage();
  }
 if (n>10000000)  {printf("\nyour number is too big\n");exit(0);}
 for (i=3;i<=n;i+=2) {
  ctr+=isprime(i);
  }
 printf("\nn / # primes < n = %d / %d = %3.7f\n",n,ctr,1.0*n/ctr);
 printf("\nln(%d) = %3.7f\n",n,log(n));
 return 0;
 }