Merge pull request #16 from CrumbleZ/master

Performance improvements

Author: rawktron

recipes/Python/117119_Sieve_of_Eratosthenes/recipe-117119.py

@@ -1,18 +1,19 @@
 # Sieve of Eratosthenes
-# David Eppstein, UC Irvine, 28 Feb 2002
+# Originaly made by : David Eppstein, UC Irvine, 28 Feb 2002
+# Performance improvements : Gabriel Freitas, 7 Oct 2017
 
-from __future__ import generators
+from itertools import count
 
 def eratosthenes():
-	'''Yields the sequence of prime numbers via the Sieve of Eratosthenes.'''
-	D = {}  # map composite integers to primes witnessing their compositeness
-	q = 2   # first integer to test for primality
-	while 1:
-		if q not in D:
-			yield q        # not marked composite, must be prime
-			D[q*q] = [q]   # first multiple of q not already marked
-		else:
-			for p in D[q]: # move each witness to its next multiple
-				D.setdefault(p+q,[]).append(p)
-			del D[q]       # no longer need D[q], free memory
-		q += 1
+    """Yields the sequence of prime numbers via the Sieve of Eratosthenes"""
+    yield 2 # force yield the first prime number
+
+    D = {}  # map composite integers to primes witnessing their compositeness
+    for q in count(start=3, step=2):
+        if q not in D:
+            yield q        # not marked composite, must be prime
+            D[q*q] = [q]   # first multiple of q not already marked
+        else:
+            for p in D[q]: # move each witness to its next odd multiple
+                D.setdefault(2*p+q,[]).append(p)
+            del D[q]       # no longer need D[q], free memory