Implementation of sieve of eratosthenes

Author: OmkarPathak

pygorithm/math/sieve_of_eratosthenes.py

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+# Author: OMKAR PATHAK
+# Created at: 16th August 2017
+
+# Sieve of Eratosthenes is one of the efficient algorithms to find all the prime numbers upto n, where n can be
+# upto 10 million. This algorithm is very efficient and fast and hence is preferred by many competitive programmers.
+
+# Algo:
+# 1. Create a list of consecutive integers from 2 to n: (2, 3, 4, …, n).
+# 2. Initially, let p equal 2, the first prime number.
+# 3. Starting from p, count up in increments of p and mark each of these numbers greater than p itself in the list.
+#    These numbers will be 2p, 3p, 4p, etc.; note that some of them may have already been marked.
+# 4. Find the first number greater than p in the list that is not marked. If there was no such number, stop. Otherwise,
+#    let p now equal this number (which is the next prime), and repeat from step 3.
+# When the algorithm terminates, all the numbers in the list that are not marked (i.e are True) are prime.
+
+def sieve_of_eratosthenes(n):
+    ''' function to find and print prime numbers upto the specified number
+
+        :param n: upper limit for finding all primes less than this value
+    '''
+    primes = [True] * (n + 1)
+    p = 2                   # because p is the smallest prime
+
+    while(p * p <= n):
+        # if p is not marked as False, this it is a prime
+        if(primes[p]) == True:
+            # mark all the multiples of number as False
+            for i in range(p * 2, n + 1, p):
+                primes[i] = False
+
+        p += 1
+
+    # getting all primes
+    primes = [element for element in range(2, n) if primes[element]]
+
+    return primes
+
+def get_code():
+    """ returns the code for the current class """
+    import inspect
+    return inspect.getsource(sieve_of_eratosthenes)