
from __future__ import annotations

import math







def 							A__       (    lowerCamelCase    )	->						Dict:



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


lowerCamelCase_    :			Tuple    =	[num for num in range(3, 10_00_01, 2) if not is_prime(num)]







def 							A__       (    lowerCamelCase    )	->						Tuple:



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

				UpperCamelCase_:				Union[str, Any]						=    []
				for num in range(len(__a    )    ):
								UpperCamelCase_:				Tuple						=    0
								while 2 * i * i <= odd_composites[num]:
												UpperCamelCase_:				Union[str, Any]						=    odd_composites[num] - 2 * i * i
												if is_prime(__a    ):
																break
												i += 1
								else:
												list_nums.append(odd_composites[num]    )
												if len(__a    ) == n:
																return list_nums

				return []







def 							A__       (    )	->						Dict:
				return compute_nums(1    )[0]


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











"""simple docstring"""







from math import ceil, sqrt

def     UpperCAmelCase_					(				__a   :			int = 1_00_00_00						):




			'''simple docstring'''



			_lowerCamelCase					:					Tuple	       =    0

			for outer_width in range(3      ,							(limit // 4) + 2						):
						if outer_width**2 > limit:
									_lowerCamelCase					:					Optional[int]	       =    max(ceil(sqrt(outer_width**2 - limit						)						)      ,							1						)
						else:
									_lowerCamelCase					:					Any	       =    1
						if (outer_width - hole_width_lower_bound) % 2:
									hole_width_lower_bound += 1

						answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

			return answer


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





