Requirement 1:

Find filenames within a directory that look like '\A\d+\.jpg\z'. (I prefer \A and \z over ^ and $ as \A and \z match 'beginning of string' and 'end of string' as opposed to 'beginning of line' and 'end of line')

my(@filenames, $directory);
opendir($directory, $directory_path)
    or die "opendir of $directory_path failed: $!\n";
@filenames = grep /\A\d+\.jpg\z/, readdir($directory);
closedir($directory);
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Requirement 2:

Extend filenames such that they follow the form '\A\d{6,}\z'.

$filename = sprintf("%06d.jpg", $1) if $filename =~ /\A(\d+)\.jpg\z/;

Requirement 3:

Creating directory (if it does not already exist) and moving files into the directory.

use File::Spec;
-d $subdir_path
    or mkdir($subdir_path, 0777)
        or die "mkdir of $subdir_path failed: $!\n";
rename($filename, File::Spec->catfile($subdir_path, $filename))
    or die "rename of $filename failed: $!\n";
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Requirement 4:

Matching the first three (or more?) digits in the string.

$filename =~ /\A(\d*)\d{3}\.jpg\z/; # result stored in $1

Final Solution:

Putting this all together, we get:

use File::Spec;

for my $directory_path (@ARGV) {
    my $directory;
    my @filenames;

    # Determine @filenames to work with in $directory_path.
    opendir($directory, $directory_path)
        or die "opendir of $directory_path failed: $!\n";
    @filenames = grep /\A\d+\.jpg\z/, readdir($directory);
    closedir($directory);

    for (@filenames) {
        my($basename, $prefix) = /\A((.+).{3})\.jpg\z/s or next;
        my $subdir_path = File::Spec->catdir($directory_path, $prefix)
+;

        # Create the subdir if it does not yet exist.
        -d $subdir_path
            or mkdir($subdir_path, 0777)
                or die "mkdir of $subdir_path failed: $!\n";

        my $old_path = File::Spec->catfile($directory_path, $_);
        my $new_path = File::Spec->catfile($subdir_path, sprintf("%06d
+.jpg", $basename));

        # Move the file to the subdir.
        rename($old_path, $new_path)
            or die "rename of $old_path to $new_path failed: $!\n";

    }
}
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Edit to by tye to remove PRE tags around CODE tags