#### Prime Sieve Eratosthenes

p
"""
Sieve of Eratosthenes

Input: n = 10
Output: 2 3 5 7

Input: n = 20
Output: 2 3 5 7 11 13 17 19

you can read in detail about this at
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

def prime_sieve_eratosthenes(num: int) -> list[int]:
"""
Print the prime numbers up to n

>>> prime_sieve_eratosthenes(10)
[2, 3, 5, 7]
>>> prime_sieve_eratosthenes(20)
[2, 3, 5, 7, 11, 13, 17, 19]
>>> prime_sieve_eratosthenes(2)
[2]
>>> prime_sieve_eratosthenes(1)
[]
>>> prime_sieve_eratosthenes(-1)
Traceback (most recent call last):
...
ValueError: Input must be a positive integer
"""

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

primes = [True] * (num + 1)

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

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

if __name__ == "__main__":
import doctest

doctest.testmod()

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