# use the actual error for open
open(FILE, $filename)  || die "Error opening $filename: $!"; 

my ( $word, $count ); # move these out of the loop

while (defined ($line = <FILE>))
{
    if ($line =~ /^# word (\d+)/) # tighten up regex a bit
    {
    	if( defined $word )
    	{
            # print the results for the previous block
            print "the word number is: $word\n";
    	    print "number of text = $count\n";
    	}

        $word = $1;
        $count = 0;
    }
    elsif ($line !~ /#/)
    {
        $count++;
    }
}

# print the results for the last block of data before eof
print "the word number is: $word\n";
print "number of text = $count\n";


** output from your example data **

the word number is: 26871
number of text = 3
the word number is: 26872
number of text = 2