I recently realized the power of base-1 numbers. They don't have the arbitrary range limitations of Perl's regular number representations while converting between the two is nearly trivial. Plus finding prime base-1 numbers is particularly compact code in Perl. And when the primality test fails you are also handed some factors! So base-1 numbers are perfect for finding prime factorizations! They aren't very space efficient, unfortunately (hey, no one's perfect).

So factor1() returns the prime factorizations of base-1 numbers (as base-1 numbers). factor10() just converts a base-10 number into a base-1 number so factor1() can factor it and then converts the returned list of base-1 factors into base 10 again.

One line of test code is included that factors any base-10 numbers given on the command line.

Now updated to be faster!

#!/usr/bin/perl -w
use strict;

sub factor1 {
    return @_  if  $_[0] !~ /^(..+?)\1+$/;
    return map { factor1($_) }
        ( "$1", $_[0] =~ s/$1/1/g, $_[0] )[0,-1];
}

sub factor10 {
    return map {length} factor1( 1x$_[0] );
}

print join $/, map { join " ", factor10($_) } @ARGV;
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