The concept of an "oracle algorithm" (an algorithm that gets to ask questions to an "oracle", thus hopefully increasing its computational power) has been useful for abstract computational complexity arguments. My QUESTION: has it ever been actually *directly* useful as an algorithm? Reason I'm asking is, my alleged new integer factoring algorithm SMODA is an oracle algorithm, and does claim to be directly useful. Its oracle is a quite small -- and nice to have, but it's apparently rather hard to produce it -- database. So I wasn't sure what to make of that, and then I thought a bit and wasn't able to think of anybody else who'd ever made an algorithm with these properties. Although quite likely that is merely because I am ignorant.