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Yes it is off topic a little, but the main idea is still good - plug the people that are helping you.
Say the Vatican is linking to you. Maybe someone out there is linking to the wrong domain name - or an outdated one. You write the person and say - FYI - your link pointing to the vatican is out of date - it should be blahblahblah.
This works especially well if someone up the chain is an educational institution. They don't want to look like idiots and I have seen them try to link to stuff on their C:/drive. A little helping hand will help you out as well. Of course if the others are your competitors - then you have something to think about.
This happens much more than you would expect.
The vatican has an error on it:
[vatican.va...]
One of the links on their doesn't work.
Magnum Matrimonii Sacramentum
If that somehow influenced your site - a little note to the WM would probably be greatly appreciated and sometimes - depending on the situation - you can get a direct link from them as well.
It toook me less than 3 minutes to find the error.
There are six other at least and I have only crawled less than 10% of the site.
Just a suggestion.
Also think of the good work you will be doing by make the internet a beter place.
p.s. It is highly frowned upon to give examples of others sites errors. As the pope forgave the person who shot him - I don't think he will mind as it is only mentioned for non malicious reasons.
I have noticed that with a PR 4 or 5, if a site goes over a 12% increase it is predicted to move to a PR 5 or 6, respectively.
I assume that means 12% of increase in links?