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I guess lot's of webmasters and automated scripts make up a huge percentage of their search. I am pretty sure it's for most SE that use "link:" syntax.
Or maybe it was just that one time, when someone was running a program to check amount of links...
This makes 1/30 of all requests to ATW just link checking which is mostly a webmaster tool...
So if google does 250 million searches a day and has the same rate of link: searches, that would make 8.3 million searches.
I then, searched for "link:" and "link.all" searches.
There were 78 searches requested out of 10000, that included "link:" syntax.
That is way less then I approximated above, but still a lot if you think about it!