added some notes

1 files changed, 38 insertions, 0 deletions

diff --git a/challenge-139/james-smith/perl/ch-2.pl b/challenge-139/james-smith/perl/ch-2.pl
index c828aefea7..f431910856 100644
--- a/challenge-139/james-smith/perl/ch-2.pl
+++ b/challenge-139/james-smith/perl/ch-2.pl
@@ -6,14 +6,52 @@ use feature qw(say);
 
 my( $N, @primes, @long_primes ) = ( $ARGV[0]||5 );
 
+##
+## We know 2 isn't a long prime, and also we are
+## only looking at odd numbers so we don't have
+## to worry about the special case of 2.
+##
+## Starting at the 3 we loop through the odd numbers
+## Looking to see if the number is composite {has
+## at least 1 prime factor lower than $p}.
+##
+## Skip to next number if it is (line 2)
+##
+## If it has the long_prime property we add it
+## to the list of long primes (line 3)
+## We also add it to the primes list (line 4)
+##
+## We exit the loop when we have the appropriate
+## number of long primes
+##
+
 O: for( my $p=3; @long_primes<$N; $p+=2 ) {
   ($p % $_) || (next O) for @primes;
   push @long_primes, $p if $p - rec_len($p) == 1;
   push @primes,      $p;
 }
 
+
+##
+## Output the long primes
+##
+
 say $_ for @long_primes;
 
+##
+## We use long division here to compute the reciprocal
+## of $D, to ensure we get a repeating pattern - we
+## compute the 2$D + length $D digits as the repeating
+## pattern will comprise of a number of 0s followed by
+## the repeating pattern (which has to be at least
+## 2$D-2 long.
+##
+## This division is done in line 2.
+##
+## The 3rd line finds the shortest repeating sequence
+## tied to the end of this string, and returns its
+## length
+##
 sub rec_len {
   my( $D, $N, $s ) = ( shift, 1, '' );
   $s.=int($N/$D),$N%=$D,$N.=0 for 0..2*$D+length $D;