This is not tested:

my ($count, $word);
while (<>) {
    $count++ unless /#/;        # or maybe /^#/ would be better?
    if (/^# word (\d+)/) {      # or \S+, etc. -- depending on what's 
+a valid word
        print "word $word\nnumber of text = $count\n" if defined $word
+;
        $count = 0;
        $word  = $1;
    }
}
print "word $word\nnumber of text = $count\n" if defined $word;    # h
+andle leftover word.
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You can move the conditional output print to a function if duplicating the code bothers you.