Task — Brilliant numbers

Write a script to generate first 20 Brilliant Numbers. Brilliant numbers are numbers with exactly two prime factors with the same number of digits.

Examples

Example 1:
24287 = 149 x 163

Example 2:
24289 = 107 x 227

Analysis

The criteria for brilliant numbers sound easy to met. For example, there are 21 2-digit prime numbers, yielding 231 brilliant numbers ranging from 441 to 9409, so they're not rare.

The ever-helpful Math::Prime::Util has a function factor($n) which returns a list of prime factors of its argument, so the algorithm looks like this:

• Loop $test from 1 to something big until we've found 20 brilliant numbers
• Get the prime factors (pf) of $test
• Skip to the next $test unless pf contains exactly 2 same-length members
• Else $test is brilliant

That generates the desired 20 numbers in microseconds, 2000 in under a second and 20 000 in under 15 seconds on my lowly Raspberry Pi. The 20 000th brilliant number is 2733299, which is 1117 x 2447.

Script

#!/usr/bin/perl

# Peter Campbell Smith - 2022-06-13
# PWC 169 task 1

use v5.28;
use strict;
use warnings;
use utf8;
use Math::Prime::Util qw[factor];

my ($test, @pf, @result, $count, $j, $j_max);

# loop till done
$j = 0;
for ($test = 1, $count = 0; $count < 20; $test ++) {
    @pf = factor($test);
    
    # test for brilliance
    next unless (scalar @pf == 2 and length($pf[0]) == length($pf[1]));
    
    # accumulate answers
    $result[$j ++] = $test;
    $count ++;
}

# tell the world
for ($j = 0; $j < @result; $j ++) {
    print $result[$j];
    print ', ' unless $j == @result - 1;
    say '' if $j % 10 == 9;
}   

Output

4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 
121, 143, 169, 187, 209, 221, 247, 253, 289, 299