



from __future__ import annotations

import math

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


UpperCAmelCase_		 =					[num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     list[int]:
   if not isinstance(_snake_case	,   _snake_case				):
      raise ValueError('''n must be an integer'''				)
   if n <= 0:
      raise ValueError('''n must be >= 0'''				)

   _A      =       []
   for num in range(len(_snake_case				)				):
      _A      =       0
      while 2 * i * i <= odd_composites[num]:
         _A      =       odd_composites[num] - 2 * i * i
         if is_prime(_snake_case				):
            break
         i += 1
      else:
         list_nums.append(odd_composites[num]				)
         if len(_snake_case				) == n:
            return list_nums

   return []

def 	SCREAMING_SNAKE_CASE_							(	)  ->     int:
   return compute_nums(1				)[0]


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








import itertools
import math

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

def 	SCREAMING_SNAKE_CASE_							(	)  ->     Dict:
   _A      =       2
   while True:
      if is_prime(_snake_case				):
         yield num
      num += 1

def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int = 10_001				)  ->     int:
   return next(itertools.islice(prime_generator()	,   nth - 1	,   _snake_case				)				)


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



