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

typedef struct {
  int* digits;
  int length;
} Transcendental;

Transcendental e;


void calcDigits(unsigned int numDigits) {
  // declare dynamic array to hold digits of e
  e.length = numDigits;
  e.digits = (int *) malloc(numDigits);

  // spigot algorithm
  int N = numDigits + 9, a[numDigits+9], x = 0;
  for (int n = N - 1; n > 0; --n) {
      a[n] = 1;
  }
  a[1] = 2, a[0] = 0;
  while (N > 9) {
      int n = N--;
      while (--n) {
          a[n] = x % n;
          x = 10 * a[n-1] + x/n;
      }
      // populate array with digits
      e.digits[(numDigits+8) - N] = x%10;
  }
}

bool isPrime(unsigned long n) {
  // screen out numbers that can't be prime
  if (n != 2 && n != 3 && n % 6 != 1 && n % 6 != 5) {
    return false;
  }
  // check factors up to square root
  for (unsigned int i=3; (unsigned long) i * i <= n; i++) {
    if (n % i == 0) return false;
  }
  return true;
}

int main() {
  //get first 1000 digits of e
  calcDigits(1000);
  int pos = 0;
  unsigned long currentTen = 2;
  while(pos < e.length){
    currentTen = (currentTen % 1000000000) * 10 + e.digits[pos];
    if(pos >= 9 && isPrime(currentTen)) {
      printf("found! %lu\n", currentTen);
      free(e.digits);
      return 0;
    }
    pos++;
  }
  printf("failed to find :(\n");
  free(e.digits);
  return 1;
}