maths.sieve_of_eratosthenes
===========================

.. py:module:: maths.sieve_of_eratosthenes

.. autoapi-nested-parse::

   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



Functions
---------

.. autoapisummary::

   maths.sieve_of_eratosthenes.prime_sieve


Module Contents
---------------

.. py:function:: 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)
   []