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

Main();
exit();

sub repDig
{
    my( $den, $num )= @_;
    $num ||= 1;
    my $rem= $num % $den;
    my %seen;
    my $rep= '';
    while(  1  ) {
        $rem *= 10;
        last
            if  exists $seen{$rem};
        $seen{$rem}= length( $rep );
        $rep .= int( $rem / $den );
        $rem %= $den;
    }
    substr( $rep, 0, $seen{$rem} )= '';
    return $rep;
}


sub factor
{
    my( $r )= @_;
    my $f= '';
    my @f;
    my $p= 2;
    while( 1 < $r ) {
        my $q= int( $r / $p );
        last
            if  $q < $p;
        my $e= 0;
        while(  $r == $q*$p  &&  $q  ) {
            $e++;
            $r= $q;
            $q= int( $r / $p );
        }
        if(  $e  ) {
            push @f, $p;
            $f .= "*$p";
            $f .= "^$e"
                if  1 < $e;
        }
        $p += 2==$p ? 1 : 2;
    }
    if(  1 < $r  ||  ! @f  ) {
        push @f, $r;
        $f .= "*$r";
    }
    substr( $f, 0, 1 )= '';
    return $f, @f;
}


sub Main
{
    my $dem= 1;
    my %r;
    while( 1 ) {
        my( $f, @f )= factor( ++$dem );
        my $r= repDig( $dem );
        $r= $r ? length($r) : 0;
        if(  $f eq $dem  ) {
            $r{$dem}= $r;
            next
                if  $r == $dem-1;
        } else {
            my $max= 0;
            for(  @f  ) {
                $max= $r{$_}
                    if  $max < $r{$_};
            }
            next
                if  $r == $max;
        }
        printf "%8d: 1/%s\n", $r, $f;
    }
}