add simple improved Sieve Of Eratosthenes Algorithm (TheAlgorithms#1412)

* add simple improved Sieve Of Eratosthenes Algorithm

* added doctests

* name changed

Author: ShuLaPy

maths/prime_sieve_eratosthenes.py

@@ -0,0 +1,41 @@
+'''
+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):
+    """
+    print the prime numbers upto n
+    
+    >>> prime_sieve_eratosthenes(10)
+    2 3 5 7 
+    >>> prime_sieve_eratosthenes(20)
+    2 3 5 7 11 13 17 19 
+    """
+    
+    
+    primes = [True for i in range(num + 1)]
+    p = 2
+    
+    while p * p <= num:
+        if primes[p] == True:
+            for i in range(p*p, num+1, p):
+                primes[i] = False
+        p+=1
+
+    for prime in range(2, num+1):
+        if primes[prime]:
+            print(prime, end=" ")
+
+if __name__ == "__main__":
+    num = int(input())
+    
+    prime_sieve_eratosthenes(num)