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I think a useful feature would be negative searches: searches in which at least one term is constrained to not occur (but no more than all but one terms, of course -- you wouldn't want to bring back all/almost all questions).

This would be useful both for bare terms

prime -ideal

and tags

diophantine -[elementary-number-theory]
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    $\begingroup$ Have you tried it? For me, searching "prime -ideal" works as expected! $\endgroup$ Sep 11, 2011 at 7:30
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    $\begingroup$ FWIW, Google also recognizes search operators like -. So something like site:math.stackexchange.com +prime -ideal works nicely if the built-in search is not to your taste. $\endgroup$ Sep 11, 2011 at 9:39

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I'm tempted to close this as "not a real question", because as Hendrik said in a comment:

So it appears that both of the requested features are already features....

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  • $\begingroup$ I think it was very cute to perform the searches on this question. I liked that a lot. $\endgroup$
    – davidlowryduda Mod
    Sep 11, 2011 at 15:36
  • $\begingroup$ That's fascinating, because it did not work at all in my tests (on math.se). I'll have to experiment and get back to you. $\endgroup$
    – Charles
    Sep 11, 2011 at 17:23

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