From 9e2d5b610147415c99f25fe4ff0cea2b1a832706 Mon Sep 17 00:00:00 2001
From: Correl Roush <correl@gmail.com>
Date: Mon, 12 Apr 2010 15:53:09 +0000
Subject: [PATCH] Optimized prime finding

git-svn-id: file:///srv/svn/euler@30 e5f4c3ec-3c0c-11df-b522-21efaa4426b5
---
 007.py | 40 ++++++++++++++++++++++++++++++----------
 1 file changed, 30 insertions(+), 10 deletions(-)

diff --git a/007.py b/007.py
index 0af7cd4..c3724e8 100644
--- a/007.py
+++ b/007.py
@@ -1,15 +1,35 @@
-def primes(limit):
+import math
+
+def is_prime(n):
+    if n == 1:
+        return False
+    if n < 4:
+        return True
+    if n % 2 == 0:
+        return False
+    if n < 9:
+        return True
+    if n % 3 == 0:
+        return False
+    
+    r = math.floor(math.sqrt(n))
+    f = 5
+    while f <= r:
+        if (n % f == 0) or (n % (f + 2) == 0):
+            return False
+        f = f + 6
+    return True
+
+def primes(max_count = 0, max_value = 0):
+    if not max_count and not max_value:
+        raise Exception('There must be a constraint on how many primes to return!')
     primes = [2]
-    i = 3
-    while len(primes) < limit:
-        is_prime = True
-        for p in primes:
-            if i % p == 0:
-                is_prime = False
-                break
-        if is_prime:
-            primes.append(i)
+    i = 1
+    while (not max_count or len(primes) < max_count) \
+    and (not max_value or i < max_value):
         i = i + 2
+        if is_prime(i):
+            primes.append(i)
     return primes
 
 if __name__ == '__main__':