From 7f8098ef774a3bb2dee4a4a3a55380218cc4a452 Mon Sep 17 00:00:00 2001
From: Correl Roush <correl@gmail.com>
Date: Fri, 10 Sep 2010 10:21:43 -0400
Subject: [PATCH] Rewrote #007 with a prime generator, updated #010 and #035
 that depend on #007

---
 e007.py | 19 +++++++++++++++++--
 e010.py | 12 +++++++++---
 e035.py | 12 ++++++------
 3 files changed, 32 insertions(+), 11 deletions(-)

diff --git a/e007.py b/e007.py
index 9e95673..e006570 100644
--- a/e007.py
+++ b/e007.py
@@ -26,6 +26,14 @@ def is_prime(n):
         f = f + 6
     return True
 
+def prime_generator():
+    i = 1
+    yield 2
+    while True:
+        i += 2
+        if is_prime(i):
+            yield i
+
 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!')
@@ -39,8 +47,15 @@ def primes(max_count = 0, max_value = 0):
     return primes
 
 def main():
-    print '6th Prime', primes(6)[-1]
-    print '10001st Prime', primes(10001)[-1]
+    i = 0
+    prime = 0
+    generator = prime_generator()
+    while i < 10000:
+        i += 1
+        prime = generator.next()
+        if i == 6:
+            print '6th Prime', prime
+    print '10001st Prime', prime
 
 if __name__ == '__main__':
     main()
diff --git a/e010.py b/e010.py
index c35677d..6a2e4fb 100644
--- a/e010.py
+++ b/e010.py
@@ -4,12 +4,18 @@ The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 Find the sum of all the primes below two million.
 """
 
-from e007 import primes;
+from e007 import prime_generator
 
 def main():
     print 'Fetching all primes for n < 2,000,000'
-    p = primes(0, 2000000)
-    print 'Sum:', sum(p)
+    total = 0
+    generator = prime_generator()
+    while True:
+        prime = generator.next()
+        if prime >= 2000000:
+            break
+        total += prime
+    print 'Sum:', total
 
 if __name__ == '__main__':
     main()
diff --git a/e035.py b/e035.py
index 4bfb312..54719b7 100644
--- a/e035.py
+++ b/e035.py
@@ -6,7 +6,7 @@ There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73
 How many circular primes are there below one million?
 """
 
-from e007 import primes
+from e007 import is_prime, prime_generator
 
 class NotCircular(Exception):
     pass
@@ -30,10 +30,10 @@ def cyclic_rotation(n):
 def main():
     MAX = 1000000
     circular_primes = []
-    print 'Generating primes for p < {0}...'.format(MAX)
-    prime_list = primes(0, MAX)
-    print 'Searching for circular primes...'
-    for prime in prime_list:
+    print 'Searching for circular primes for p < {0}...'.format(MAX)
+    for prime in prime_generator():
+        if prime >= MAX:
+            break
         try:
             # Ensure the prime *can* be circular
             if prime > 9:
@@ -41,7 +41,7 @@ def main():
                     raise NotCircular()
             # Check all permutations
             for rotation in cyclic_rotation(prime):
-                if rotation not in prime_list:
+                if not is_prime(rotation):
                     raise NotCircular()
             circular_primes.append(prime)
         except NotCircular: