diff --git a/primes32.tal b/primes32.tal
index ad03ef0..20744ce 100644
--- a/primes32.tal
+++ b/primes32.tal
@@ -1,22 +1,27 @@
-( primes32.tal )
-( )
+( primes32.tal                                         )
+(                                                      )
 ( Uses a simple trial-divion method to find primes.    )
-( )
+(                                                      )
 ( To determine if x is prime we:                       )
 ( 1. Check if x is 2 (prime)                           )
 ( 2. Check if x is even (not prime)                    )
-( 3. Starting with i=3, we see if x%i is 0             )
-(   a. We increment i by 2 to avoid even i             )
+( 3. Check if x is 3 (prime)                           )
+( 4. Starting with i=5, we see if x%i is 0             )
+(   a. We alternately increment i by 2 and 4           )
 (   b. We stop when x < i*i or i=0xffff                )
-( 4. If we didn't find an i, x is prime.               )
-( )
+( 5. If we didn't find an i, x is prime.               )
+(                                                      )
+( The reason we alternate our increment is because we  )
+( know that x%6 must equal 1 or 5. if x%6 was 3 then x )
+( would be divisible by 3.                             )
+(                                                      )
 ( This method can be fast for some large composite     )
 ( numbers but is slower for large primes.              )
-( )
+(                                                      )
 ( On my machine, checking 0x7fffffff took 0.5 seconds  )
 ( and checking 0xfffffffb took 0.9 seconds. Both are   )
 ( prime numbers.                                       )
-( )
+(                                                      )
 ( Smaller primes also run fairly quickly: 0x17b5d was  )
 ( determined to be prime in 0.02 seconds.              )
 
@@ -32,7 +37,7 @@
     #fffe #0001
     OVR2 OVR2 ;is-prime32 JSR2 ( test for primality )
     STH ;emit-long JSR2 SPACE STHr EMIT-BYTE NEWLINE ( output )
-    #00 DIV #00 ( exit with /0 to make timing easier )
+    #00 #00 DIV ( exit with /0 to make timing easier )
     BRK
 
 ( include 32-bit math library )