From 483cd3629d42acbf3909cf534f5a9224f292cbeb Mon Sep 17 00:00:00 2001
From: James Raikes <James.Raikes@Shield-group.com>
Date: Thu, 14 Jul 2016 15:45:14 +0100
Subject: [PATCH] Started Problem 10 Made improvements (incomplete) to Problem
 7

---
 problem10.py |  0
 problem7.py  | 27 +++++++++++++++++----------
 2 files changed, 17 insertions(+), 10 deletions(-)
 create mode 100644 problem10.py

diff --git a/problem10.py b/problem10.py
new file mode 100644
index 0000000..e69de29
diff --git a/problem7.py b/problem7.py
index 8295db8..f3559cc 100644
--- a/problem7.py
+++ b/problem7.py
@@ -5,19 +5,22 @@
 # efficiently check for primes.
 # Divide by 2, 3, NOT 4, 5, NOT 6, 7 etc
 
-def is_prime(n):
-    '''v2, only test odd numbers up to root(n) inclusive'''
-    divisors = [2]
-    divisors.extend(list(range(3, int(n ** 0.5) + 1, 2)))
-    for i in divisors:
-        if not n % i:
-            return False
+def is_prime(test_num):
+    '''Test a number for primality.
+    
+    v3, test divisible by 2 or 3 then 6k+/-1'''
+    if test_num == 1: return False
+    if test_num in (2, 3): return True
+    if not (test_num % 2 and test_num % 3):
+        return False
     return True
 
 
-def main():
-    '''v1, tests all numbers for primality'''
-    prime_no = 10001
+def prime_generator(n):
+    '''Generate the nth prime number
+    
+    v1, tests all numbers for primality'''
+    prime_no = n
     prime_count = 0
     test_number = 0
     while prime_count < prime_no:
@@ -26,6 +29,10 @@ def main():
             prime_count += 1
     print(test_number)
 
+def main():
+    prime_generator(1)
+    prime_generator(10001)
+
 if __name__ == "__main__":
     main()