solutions

2 files changed, 63 insertions, 0 deletions

diff --git a/challenge-167/james-smith/perl/ch-1.pl b/challenge-167/james-smith/perl/ch-1.pl
new file mode 100644
index 0000000000..ba6a2a7599
--- /dev/null
+++ b/challenge-167/james-smith/perl/ch-1.pl
@@ -0,0 +1,36 @@
+#!/usr/local/bin/perl
+
+use strict;
+
+use warnings;
+use feature qw(say);
+use Test::More;
+use Benchmark qw(cmpthese timethis);
+use Data::Dumper qw(Dumper);
+use Math::Prime::Util qw(next_prime is_prime);
+
+my($p,$N,@res) = (99,10);
+
+# Cannot raise $N above 10 as the 11th value is:
+#   1,111,111,111,111,111,111
+# which is 5.5 trillion times larger than the 10th value...
+
+O: while( @res < $N ) {
+    ## Get the next prime - skip to next one if contains an even digit
+    ## As each digit is used as the last digit we know that this is not
+    ## a circular prime... (also skip 5 for a similar reason)
+  next O if ($p = next_prime $p)=~/[024568]/;
+    ## Split the string into consituent numbers...
+  my @q = split//, $p;
+    ## Check $p is the lowest of the permutations
+    ## Here @q starts out as the list of digits - but gets assigned the
+    ## list of rotations... This avoids us using a cache to see if we
+    ## have seen that combination of digits - slower but more memory
+    ## efficient...
+    ## If it is we then check to see if all are prime!
+  push @res, $p unless
+    ( grep { $p>$_ } @q = map { push @q, shift @q; join '',@q } 2..@q )
+    || grep { !is_prime( $_ ) } @q;
+}
+say for @res;
+
diff --git a/challenge-167/james-smith/perl/ch-2.pl b/challenge-167/james-smith/perl/ch-2.pl
new file mode 100644
index 0000000000..fd31b54b0d
--- /dev/null
+++ b/challenge-167/james-smith/perl/ch-2.pl
@@ -0,0 +1,27 @@
+#!/usr/local/bin/perl
+
+use strict;
+
+use warnings;
+use feature qw(say);
+use Const::Fast qw(const);
+
+const my $PI => 3.1415926535897932384626433832;
+const my $RP => 2.5066282746310002416123552393;
+const my $EP => 0.000000000001;
+const my $X  => 0.99999999999980993;
+const my @PV => (
+  676.5203681218851,  -1259.1392167224028,    771.32342877765313,     -176.61502916214059,
+   12.507343278686905,   -0.13857109526572012,  9.9843695780195716e-6,   1.5056327351493116e-7,
+);
+
+say sprintf( '%5.2f - %30.4f', $_/2, gamma($_/2) ) =~ s{[.]0000$}{}r  for -40..40;
+
+sub gamma {
+  my($i,$x,$z)=(0,$X,$_[0]);
+  return ($z<=0 && abs($z-int$z)<$EP) ? 'inf'
+       : $z < 0.5                     ? $PI / sin($PI*$z) * gamma( 1-$z )
+       : [map({$x+=$_/($z+$i++)}@PV),abs(($i=$RP*($i=$z+@PV-1.5)**($z-0.5)*exp(-$i)*$x)-int$i)<$EP?int$i:$i]->[-1]
+       ;
+}
+