Improve solution for problem 46

C/p046.c

@@ -1,3 +1,16 @@
+/* It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
+ *
+ * 9 = 7 + 2×1^2
+ * 15 = 7 + 2×2^2
+ * 21 = 3 + 2×3^2
+ * 25 = 7 + 2×3^2
+ * 27 = 19 + 2×2^2
+ * 33 = 31 + 2×1^2
+ *
+ * It turns out that the conjecture was false.
+ *
+ * What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?*/
+
 #include <stdio.h>
 #include <stdlib.h>
 #include <math.h>
@@ -24,6 +37,9 @@ int main(int argc, char **argv)
       return 1;
    }
 
+   /* For every odd number, check if it's prime, if it is check
+    * if it satisfies the Goldbach property. Continue until the 
+    * first number that doesn't is found.*/
    for(i = 3; !found && i < N; i += 2)
    {
       if(!primes[i])
@@ -53,12 +69,15 @@ int goldbach(int n)
 {
    int i, j, tmp;
 
-   for(i = 2; i < n; i++)
+   /* Check every prime smaller than n.*/
+   for(i = 3; i < n; i += 2)
    {
       if(primes[i])
       {
          j = 1;
 
+         /* Check if summing twice a square to the prime number
+          * gives n. Return 1 when succeeding.*/
          do
          {
             tmp = i + 2 * j * j;
@@ -73,5 +92,6 @@ int goldbach(int n)
       }
    }
 
+   /* Return 0 if no solution is found.*/
    return 0;
 }

Python/p046.py

@@ -6,7 +6,7 @@ from projecteuler import sieve
 def goldbach(n):
     global primes
 
-    for i in range(2, n):
+    for i in range(3, n, 2):
         if primes[i] == 1:
             j = 1