Add doctest to maths/sieve_of_eratosthenes and remove other/finding_primes

maths/sieve_of_eratosthenes.py

@@ -1,19 +1,53 @@
-"""Sieve of Eratosthones."""
+# -*- coding: utf-8 -*-
+
+"""
+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):
-    """Sieve of Eratosthones."""
+    """
+    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)
     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):