




from __future__ import annotations

import math





def        __UpperCAmelCase						(							lowerCamelCase_ :     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(lowerCamelCase_  ) + 1  )  ,							6  ):
						if number % i == 0 or number % (i + 2) == 0:
									return False
			return True


UpperCamelCase__ :   List[str]						=							[num for num in range(3, 10_00_01, 2) if not is_prime(num)]





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







			"""simple docstring"""





			if not isinstance(lowerCamelCase_  ,							lowerCamelCase_  ):
						raise ValueError('n must be an integer'  )
			if n <= 0:
						raise ValueError('n must be >= 0'  )

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

			return []





def        __UpperCAmelCase						(							)       ->  int:







			"""simple docstring"""





			return compute_nums(1  )[0]


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








def 	SCREAMING_SNAKE_CASE_							(	_snake_case	:int				)  ->     int:
   if not isinstance(_snake_case	,   _snake_case				):
      raise ValueError('''Input must be an integer'''				)
   if input_num <= 0:
      raise ValueError('''Input must be positive'''				)
   return sum(
       divisor for divisor in range(1	,   input_num // 2 + 1				) if input_num % divisor == 0				)


if __name__ == "__main__":
   import doctest

   doctest.testmod()



