


"""simple docstring"""
import itertools
import math






def 		lowercase							(     _snake_case						:      int     )     ->bool:
	"""simple docstring"""





	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(math.sqrt(_snake_case     ) + 1     )     ,   6     ):
		if number % i == 0 or number % (i + 2) == 0:
			return False
	return True






def 		lowercase							(     )     ->Union[str, Any]:
	"""simple docstring"""





	__snake_case	:						Union[str, Any]						=				2
	while True:
		if is_prime(_snake_case     ):
			yield num
		num += 1






def 		lowercase							(     _snake_case						:      int = 10_001     )     ->int:
	"""simple docstring"""





	return next(itertools.islice(prime_generator()     ,   nth - 1     ,   _snake_case     )     )


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












'''simple docstring'''


import math
def 							UpperCAmelCase_  (						__lowerCamelCase					:					int ):
   lowercase_			:Dict    			= []
   lowercase_			:List[Any]    			= 2
   lowercase_			:Optional[Any]    			= int(math.sqrt(__lowerCamelCase ) )  # Size of every segment
   lowercase_			:Optional[Any]    			= [True] * (end + 1)
   lowercase_			:Dict    			= []

   while start <= end:
      if temp[start] is True:
         in_prime.append(__lowerCamelCase )
         for i in range(start * start	,end + 1	,__lowerCamelCase ):
            lowercase_			:List[str]    			= False
      start += 1
   prime += in_prime

   lowercase_			:Dict    			= end + 1
   lowercase_			:Dict    			= min(2 * end	,__lowerCamelCase )

   while low <= n:
      lowercase_			:Any    			= [True] * (high - low + 1)
      for each in in_prime:
         lowercase_			:List[Any]    			= math.floor(low / each ) * each
         if t < low:
            t += each

         for j in range(__lowerCamelCase	,high + 1	,__lowerCamelCase ):
            lowercase_			:str    			= False

      for j in range(len(__lowerCamelCase ) ):
         if temp[j] is True:
            prime.append(j + low )

      lowercase_			:Dict    			= high + 1
      lowercase_			:Dict    			= min(high + end	,__lowerCamelCase )

   return prime


print(sieve(10**6))


