Welcome to Weekly Challenge #167 167 is a safe prime. If there’s a prime number p where 2p + 1 is also prime, then p is a Sophie Germain prime and 2p + 1 is a safe prime, so 83 is the Sophie Germain prime to 167.

Task 1: Circular Prime

Submitted by: Mohammad S Anwar
Write a script to find out first 10 circular primes having at least 3 digits (base 10).

Please checkout wikipedia for more information.

A circular prime is a prime number with the property that the number generated at each intermediate step when cyclically permuting its (base 10) digits will also be prime.

Here’s the thing I had to figure out first: 113 is the first circular prime, because 131 and 311 are also prime. But because 133 is already counted, 131 and 311 don’t show up on the list.

Besides knowing and accounting for that, we need to know a number is prime (as we do every so often) and circularly permute the number. My solution involves a lot of substr, but I could easily imagine a solution involving splitting to an array and pushing and shifting elements off it.

Show Me The Code

#!/usr/bin/env perl

use strict;
use warnings;
use experimental qw{ say postderef signatures state };

my $top = 10;
my $c   = 100;
my %next;
my @primes;

OUTER: while ( scalar @primes < $top ) {
    next if $next{$c};
    if ( is_prime($c) ) {
        my @permutes = circular_permutes($c);
        my $f        = 0;
        for my $p (@permutes) { $next{$p}++; $f++ if is_prime($p); }
        next OUTER unless length $c == $f;
        push @primes, $c;
        sleep 1;
say join ', ', @primes;

sub circular_permutes ( $n ) {
    my @output;
    for my $i ( 1 .. length $n ) {
        my $d = $n;
        my $x = substr $d, 0, $i;
        substr( $d, 0, $i ) = '';
        $d .= $x;
        push @output, $d;
    return @output;

sub is_prime ($n) {
    die "Bad number $n" unless length $n;
    return 0 if $n == 0;
    return 0 if $n == 1;
    for ( 2 .. sqrt $n ) { return 0 unless $n % $_ }
    return 1;
$ time ./ch-1.pl
113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933

real    0m11.220s
user    0m0.281s
sys     0m0.047s

Task 2: Gamma Function

Submitted by: Mohammad S Anwar
Implement subroutine gamma() using the Lanczos approximation method.

I didn’t do this one.

I took Computer Science, and the tendency and history of Computer Science leans hard to being a specific subset of Mathematics. Therefore, I took a lot of math courses while working toward my CS degree. I retook a few. There are a few points where my knowledge of math helped with my work with computers, but by and large, no, it was nothing but a hinderance. I’ll contrast Statistics, which was made an optional part of the curriculum right before I would’ve been required to take it. I thought I was dodging a bullet, but that is the one course I didn’t take then that I know would’ve helped me as a developer.

Plus, I believe that the program intentionally hid the idea that Σ means for loop.

The Lanczos approximation is a large, unweildy piece of mathematics. It would take time to tease out what the variables are and what the things we need to do, and that doesn’t seem too fun to me. I don’t see a way to creatively engage with this task.

Additionally, Ryan Thompson goes deep into the issue, which is both great and a problem, especially as Mohammad linked to it within the challenge. Reading it began to feel like cribbing someone else’s test answer, and I don’t need to cheat on a test I’m taking for fun.

I wish everyone else the best of luck, and hope that the Perl Review will cover it.

If you have any questions or comments, I would be glad to hear it. Ask me on Twitter or make an issue on my blog repo.