#### Sieve of Eratosthenes

"""
Sieve of Eratosthones

The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
equal to a given value.
Illustration:
Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Also thanks to Dmitry (https://github.com/LizardWizzard) for finding the problem
"""
from __future__ import annotations

import math

def prime_sieve(num: int) -> list[int]:
"""
Returns a list with all prime numbers up to n.

>>> prime_sieve(50)
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
>>> prime_sieve(25)
[2, 3, 5, 7, 11, 13, 17, 19, 23]
>>> prime_sieve(10)
[2, 3, 5, 7]
>>> prime_sieve(9)
[2, 3, 5, 7]
>>> prime_sieve(2)

>>> prime_sieve(1)
[]
"""

if num <= 0:
msg = f"{num}: Invalid input, please enter a positive integer."
raise ValueError(msg)

sieve = [True] * (num + 1)
prime = []
start = 2
end = int(math.sqrt(num))

while start <= end:
# If start is a prime
if sieve[start] is True:
prime.append(start)

# Set multiples of start be False
for i in range(start * start, num + 1, start):
if sieve[i] is True:
sieve[i] = False

start += 1

for j in range(end + 1, num + 1):
if sieve[j] is True:
prime.append(j)

return prime

if __name__ == "__main__":
print(prime_sieve(int(input("Enter a positive integer: ").strip())))  