added shebangs

Author: phsteve

p1.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 #Find the sum of all the multiples of 3 or 5 below 1000.
 
 sum = 0

p10.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 #Find the sum of all primes below two million
 #Answer: 142913828922
 

p2.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 #Project Euler problem #2
 
 #Find the sum of all even terms in the Fibonacci sequence that do not exceed four million

p3.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 #Project Euler #3
 
 #What is the largest prime factor of the number 600851475143?
@@ -8,15 +10,10 @@
 
 import prime_tools
 
-#Compare a brute force method vs a method that uses a sieve of Eratosthenes to
+#Compare a brute force method vs a method that uses a sieve of Eratosthenes
 
 num = 600851475143
 
-# def find_2_factors(num):
-#     for d in range(2, int(math.sqrt(num))):
-#         if num % d == 0:
-#             return [num/d, d]
-
 def brute_factor(num):
     prime_factors = []
     found_factors = [num]

p6.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 # Find the difference between the sum of the squares of the first 100 natural
 # numbers and the square of the sum
 

p7.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 #Project Euler #7
 
 #What's the 10001st prime number?

p8.py

@@ -1,3 +1,5 @@
+#!/usr/bin/python
+
 #Find the greatest product of five consecutive digits in the 100 digit number
 n = str(7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450)
 #Answer = 40824

prime_tools.py

@@ -1,18 +1,20 @@
+#!/usr/bin/python
+
 #Collection of useful tools for working with prime numbers
 
 import math
 
 def sieve(n):
     #creates a Sieve of Eratosthenes from 2 to n-1
     #Sieve is a dictionary where True indicates prime and False indicates nonprime
-    sieve = dict.fromkeys(range(2, n), True)
+    sv = dict.fromkeys(range(2, n), True)
     for num in range(2, int(math.sqrt(n))):
-        if sieve[num]:
+        if sv[num]:
             #print "checking multiples of %d" %(num)
             for i in range(2, n/num + 1):
                 #print "     %d is not prime, marking False" %(num * i)
-                sieve[num * i] = False
-    return sieve
+                sv[num * i] = False
+    return sv
 
 def isprime(num):
     #Brute force check if a number is prime by checking divisibility