Probability of randomly choosing an integer power

gistfile1.txt

use v6;

sub is-integer-power($n) {
    for 2..($n.sqrt.floor) -> $m {
        my $c = $n;
        my $count = 0;
        while $c > 1 {
            last unless $c %% $m;
            $c div= $m;
            $count++;
        }
        if $c == 1 {
            # say "$n == $m ** $count (check { $m ** $count })";
            return True;
        }
    }
    return False;
}

my @powers-of-ten = 1, 10, 100 ... *;

for @powers-of-ten -> $pot {
    my $number-of-integer-powers = (1..$pot).grep({ is-integer-power($_) });
    say "$pot samples, { $number-of-integer-powers / $pot } probability";
}

10 samples, 0.3 probability
100 samples, 0.12 probability
1000 samples, 0.04 probability
10000 samples, 0.0124 probability
100000 samples, 0.00366 probability