




from __future__ import annotations

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


__A						:							Optional[int]						      =  [num for num in range(3, 1_0_0_0_0_1, 2) if not is_prime(num)]
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			if not isinstance(SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE   ):
						raise ValueError("""n must be an integer"""   )
			if n <= 0:
						raise ValueError("""n must be >= 0"""   )

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

			return []
def 					lowerCamelCase_    (    ):
			'''simple docstring'''
			return compute_nums(1   )[0]


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












from __future__ import annotations

import typing
from collections.abc import Iterable

import numpy as np

__A						:							Dict							=  typing.Union[Iterable[float], Iterable[int], np.ndarray]  # noqa: UP007
__A						:							Tuple							=  typing.Union[np.floataa, int, float]  # noqa: UP007
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			return np.sqrt(np.sum((np.asarray(SCREAMING_SNAKE_CASE   ) - np.asarray(SCREAMING_SNAKE_CASE   )) ** 2   )   )
def 					lowerCamelCase_    (    SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE   ):
			'''simple docstring'''
			return sum((va - va) ** 2 for va, va in zip(SCREAMING_SNAKE_CASE					,	SCREAMING_SNAKE_CASE   )   ) ** (1 / 2)


if __name__ == "__main__":
		def 					lowerCamelCase_    (    ):
					'''simple docstring'''
					from timeit import timeit

					print("""Without Numpy"""   )
					print(
					    timeit(
					        """euclidean_distance_no_np([1, 2, 3], [4, 5, 6])"""					,	number=1_00_00					,	globals=globals()					,	)   )
					print("""With Numpy"""   )
					print(
					    timeit(
					        """euclidean_distance([1, 2, 3], [4, 5, 6])"""					,	number=1_00_00					,	globals=globals()					,	)   )




		benchmark()






