Prophecy is not synonym for prediction. it is a "message from God" in the major theistic religions.

The only prophecies that were predictions I can think of with regard to Christianity were Jewish prophecies of a messiah. The Jewish prophets were leaders, not soothsayers.

> there's kind of an inverse relation between size and durability of religion and the number and specificity of predictions, though

I would question that - things like the Oracle at Delphi lasted a long time. So did fortune telling (mostly non-religious) around the world. How long as astrology lasted?