





def lowerCAmelCase__(__snake_case							)       ->   list[int]:







	'''simple docstring'''







	if num <= 0:
		raise ValueError('''Input must be a positive integer'''							)

	lowerCamelCase__              =	[True] * (num + 1)

	lowerCamelCase__              =	2
	while p * p <= num:
		if primes[p]:
			for i in range(p * p ,num + 1 ,__snake_case							):
				lowerCamelCase__              =	False
		p += 1

	return [prime for prime in range(2 ,num + 1							) if primes[prime]]


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			_a						=   int(input("Enter a positive integer: ").strip())
			print(prime_sieve_eratosthenes(user_num))










from __future__ import annotations





def lowerCAmelCase__(__snake_case ,__snake_case = None ,__snake_case = None							)       ->   None:







	'''simple docstring'''







	if start is None:
		lowerCamelCase__              =	0

	if end is None:
		lowerCamelCase__              =	len(__snake_case							) - 1

	if start >= end:
		return

	lowerCamelCase__              =	(start + end) // 2

	slowsort(__snake_case ,__snake_case ,__snake_case							)
	slowsort(__snake_case ,mid + 1 ,__snake_case							)

	if sequence[end] < sequence[mid]:
		lowerCamelCase__       ,			lowerCamelCase__              =	sequence[mid], sequence[end]

	slowsort(__snake_case ,__snake_case ,end - 1							)


if __name__ == "__main__":
			from doctest import testmod

			testmod()



