#include <stdint.h>
#include <stdio.h>
#include <assert.h>
#include <inttypes.h>
#include <string.h>
#include <math.h>
#include <stdbool.h>

static inline int hamming_distance(uint32_t x, uint32_t y)
{
  uint32_t val = x ^ y;
  return __builtin_popcount(val);
}

uint32_t print_list(uint32_t * nums, int len)
{
  for (uint32_t i = 0; i < len; i++) {
    printf("0x%06" PRIx32 ", ", nums[i]);
  }
  printf("\n");
}

static const int target = 14;

bool is_prime(int num) {
  if (num <= 1) return false;
  if (num <= 3) return true;

  int range = sqrt(num);
  // This is checked so that we can skip
  // middle five numbers in below loop
  if (num % 2 == 0 || num % 3 == 0)
    return false;

  for (int i = 5; i <= range; i += 6)
    if (num % i == 0 || num % (i + 2) == 0)
      return false;

  return true;
}

static uint32_t primes[1 << 24];
static int primes_length = 0;

int foo(uint32_t * nums, int len)
{
  uint32_t nums1[len + 1];

  for (uint32_t j = 0xaaaaaa; j > 1; j--) {
    if (__builtin_popcount(j) > 12 || __builtin_popcount(j) < 8) continue;
    for (int i = 0; i < len; i++) {
      if (hamming_distance(nums[i], j) < target) {
        goto next_n;
      }
    }

    memcpy(nums1, nums, (sizeof (uint32_t)) * len);
    nums1[len] = j;
    if (len + 1 >= 6) {
      print_list(&nums1[0], len + 1);
      return 1;
    }

    if (len < 6) {
      int n = foo(&nums1[0], len + 1);
    }

  next_n:
    continue;
  }

  return 0;
}

int main()
{
  for (uint32_t j = 0xaaaaaa; j > 1; j--) {
    if (__builtin_popcount(j) > 12 || __builtin_popcount(j) < 8) continue;
    if (!is_prime(j)) continue;
    primes[primes_length++] = j;
  }
  printf("%d\n", primes_length);

  foo(NULL, 0);
}