old_contents: """
  Sieve of Eratosthones
  
  The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
  equal to a given value.
  Illustration:
  https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
  Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
  
  doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
  Also thanks Dmitry (https://github.com/LizardWizzard) for finding the problem
  """
  
  
  import math
  
  
  def sieve(n):
      """
      Returns a list with all prime numbers up to n.
  
      >>> sieve(50)
      [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]
      >>> sieve(25)
      [2, 3, 5, 7, 11, 13, 17, 19, 23]
      >>> sieve(10)
      [2, 3, 5, 7]
      >>> sieve(9)
      [2, 3, 5, 7]
      >>> sieve(2)
      [2]
      >>> sieve(1)
      []
      """
  
      l = [True] * (n + 1)  # noqa: E741
      prime = []
      start = 2
      end = int(math.sqrt(n))
  
      while start <= end:
          # If start is a prime
          if l[start] is True:
              prime.append(start)
  
              # Set multiples of start be False
              for i in range(start * start, n + 1, start):
                  if l[i] is True:
                      l[i] = False
  
          start += 1
  
      for j in range(end + 1, n + 1):
          if l[j] is True:
              prime.append(j)
  
      return prime
  
  
  if __name__ == "__main__":
      print(sieve(int(input("Enter n: ").strip())))
  
new_contents: """
  Sieve of Eratosthones
  
  The sieve of Eratosthenes is an algorithm used to find prime numbers, less than or
  equal to a given value.
  Illustration:
  https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif
  Reference: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
  
  doctest provider: Bruno Simas Hadlich (https://github.com/brunohadlich)
  Also thanks to Dmitry (https://github.com/LizardWizzard) for finding the problem
  """
  
  
  import math
  from typing import List
  
  
  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)
      [2]
      >>> prime_sieve(1)
      []
      """
  
      if num <= 0:
          raise ValueError(f"{num}: Invalid input, please enter a positive integer.")
  
      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())))
  
subject: Add type hints (#2627)