




def 					UpperCAmelCase_							(      __UpperCAmelCase						:	int							)					-> list[int]:

      if num <= 0:
            raise ValueError('Input must be a positive integer'							)

      SCREAMING_SNAKE_CASE_							=			[True] * (num + 1)

      SCREAMING_SNAKE_CASE_							=			2
      while p * p <= num:
            if primes[p]:
                  for i in range(p * p			,			num + 1			,			__UpperCAmelCase							):
                        SCREAMING_SNAKE_CASE_							=			False
            p += 1

      return [prime for prime in range(2			,			num + 1							) if primes[prime]]


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   lowerCamelCase__ :   Any					=							int(input('Enter a positive integer: ').strip())
   print(prime_sieve_eratosthenes(user_num))





from math import sqrt

def 					UpperCAmelCase_							(      __UpperCAmelCase						:	int							)					-> bool:

      if 1 < number < 4:
            # 2 and 3 are primes
            return True
      elif number < 2 or number % 2 == 0 or number % 3 == 0:
            # Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
            return False

      # All primes number are in format of 6k +/- 1
      for i in range(5			,			int(sqrt(__UpperCAmelCase							) + 1							)			,			6							):
            if number % i == 0 or number % (i + 2) == 0:
                  return False
      return True

def 					UpperCAmelCase_							(      __UpperCAmelCase						:	int = 1_00_01							)					-> int:
      SCREAMING_SNAKE_CASE_							=			0
      SCREAMING_SNAKE_CASE_							=			1
      while count != nth and number < 3:
            number += 1
            if is_prime(__UpperCAmelCase							):
                  count += 1
      while count != nth:
            number += 2
            if is_prime(__UpperCAmelCase							):
                  count += 1
      return number


if __name__ == "__main__":
   print(f'''{solution() = }''')