- Added solutions by Colin Crain.

4 files changed, 204 insertions, 0 deletions

diff --git a/challenge-158/colin-crain/perl/ch-1.pl b/challenge-158/colin-crain/perl/ch-1.pl
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+#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl

+#

+#       add-another-prime-to-the-pile.pl

+#

+#       Additive Primes

+#         Submitted by: Mohammad S Anwar

+# 

+#         Write a script to find out all Additive Primes <= 100.

+# 

+#         Additive primes are prime numbers for which the sum of their

+#         decimal digits are also primes.

+# 

+#         Output

+#             2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89

+#             

+#         method

+# 

+#             You know, sometimes when I do these problems I like to

+#             pretend that I'm not good at math. Which is to say choose to

+#             I regard the problem as a computing problem, rather than a

+#             math problem, or or even more broadly a problem in search of

+#             a structure that will solve it, rather than any specific

+#             answer. 

+#             

+#             Or put another way solve a more generalized version with more

+#             unknowns. 

+#             

+#             In this problem we need a bunch of prime numbers. A quick bit

+#             of mathematical reasoning tells us 

+#                 

+#                 1. that 100 is not a additive prime, as it adds to 1

+#                 2. the that largest digit-sum we'll need to deal with is 

+#                    for the value 99, where 9 + 9 = 18. 

+#                 3. thus, using preexisting knowledge we only need to consider 

+#                    the primes 2, 3, 5, 7, 11, 13, and 17

+# 

+#             But you know what? We're going to pretend we don't know that,

+#             and instead compute as many primes as required. Along the way

+#             we'll make the upper limit user-configurable, which will

+#             allow us to find the number 102 should we wish, which by the

+#             looks of it is an addative prime. 

+# 

+#             What we'll need to do is make a lookup of primes that

+#             contains every prime less than the largest value we have

+#             tried to date. The digit sum will always be less than or

+#             equal to the value. If we exceed the last prime found, we'll

+#             expand our bounds in the list of found primes as required.

+# 

+#             We can then construct a lookup hash to check for primality.

+# 

+#             Then we can break apart the number into its digits and sum

+#             them, and do a quick lookup to see whether the result is

+#             prime. 

+#

+#       © 2022 colin crain

+## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##

+

+

+

+use warnings;

+use strict;

+use utf8;

+use feature ":5.26";

+use feature qw(signatures);

+no warnings 'experimental::signatures';

+

+use List::Util qw( sum0 );

+

+my @primes;

+my %lookup;

+my @additives;

+

+## make a closed prime iterator function

+## modified to add to the prime lookup hash

+my $pg =  sub {

+    if ( @primes < 2 ) {

+        push @primes, @primes == 0 ? 2 : 3;

+        $lookup{ $primes[-1] } = 1;

+        return $primes[-1];

+    }

+

+    my $candidate = $primes[-1] ;

+    CANDIDATE: while ( $candidate += 2 ) {

+        my $sqrt_candidate = sqrt( $candidate );

+        for my $test ( @primes ) {

+            next CANDIDATE if $candidate % $test == 0;

+            last if $test > $sqrt_candidate;

+        }

+        push @primes, $candidate;

+        $lookup{ $candidate } = 1;

+        return $candidate;

+    }

+} ;

+$pg->();        ## init the prime array with 2

+

+my $limit = shift @ARGV // 100;

+

+## look at the numbers 1 to $limit,

+## checking each for primality and primality in the digit sum

+for ( 1..$limit ) {

+    $pg->() if $primes[-1] <= $_ ;

+    next unless $lookup{$_} ;

+    my $sum = sum0( split //, $_ );

+    push @additives, $_ if  $lookup{$sum};

+}

+

+say join ', ',  @additives;

+

+

+

+ 

diff --git a/challenge-158/colin-crain/perl/ch-2.pl b/challenge-158/colin-crain/perl/ch-2.pl
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+#!/Users/colincrain/perl5/perlbrew/perls/perl-5.32.0/bin/perl

+#

+#       cubans-in-their-prime.pl

+#

+#       First Series Cuban Primes

+#         Submitted by: Mohammad S Anwar

+#         Write a script to compute first series Cuban Primes <= 1000.

+#         Please refer wikipedia page for more informations.

+# 

+#         Output:

+#             7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919.      

+#

+#       © 2022 colin crain

+## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##

+

+

+

+use warnings;

+use strict;

+use utf8;

+use feature ":5.26";

+use feature qw(signatures);

+no warnings 'experimental::signatures';

+

+

+sub nth_series_cubic ( $dif ) {

+    my @c;

+    my $x;

+    for my $y ( 1..100 ) {  

+        $x = $y + $dif;

+        push @c, ($x**3 - $y**3) / ($x - $y) ;

+    }

+    return @c;

+}

+

+sub is_prime ($num) {

+    for ( 2..sqrt $num ) {

+        return 0 unless $num % $_;

+    }

+    return 1;

+}

+

+## output section

+my $out;

+for my $diff ( 1..10 ) {

+    $out .= sprintf "  %3s  | %s\n", 

+        $diff, 

+        join ' ', grep { is_prime($_) && $_ <= 1000 } nth_series_cubic( $diff ) ;

+}

+

+say<<~"END";

+    series | sequence

+    -------+------------------------------------------

+    $out

+    END

+

diff --git a/challenge-158/colin-crain/raku/ch-1.raku b/challenge-158/colin-crain/raku/ch-1.raku
new file mode 100755
index 0000000000..f89ff21663
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+++ b/challenge-158/colin-crain/raku/ch-1.raku
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+#!/usr/bin/env perl6
+#
+#
+#       .raku
+#
+#
+#
+#       © 2022 colin crain
+## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
+
+
+
+unit sub MAIN () ;
+
+put (^100).grep(*.is-prime )
+          .grep(*.comb.sum.is-prime);
+
+        
diff --git a/challenge-158/colin-crain/raku/ch-2.raku b/challenge-158/colin-crain/raku/ch-2.raku
new file mode 100755
index 0000000000..164b06d769
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+++ b/challenge-158/colin-crain/raku/ch-2.raku
@@ -0,0 +1,19 @@
+#!/usr/bin/env perl6
+#
+#
+#       .raku
+#
+#
+#
+#       © 2022 colin crain
+## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ## ##
+
+
+
+unit sub MAIN ( $limit = 1000) ;
+
+say gather for 1..* -> $x {
+    my $n = 3 * $x² + 3 * $x + 1;
+    last if $n > $limit;
+    take $n if $n.is-prime;
+}