"person endowed with genius, especially a young child"
The overtones have been positive since the 17th century, but in Shakespeare we see the earlier sense of "omen" or "portent" for natural events such as comets portending something fearful. Both Casca and Cassius use the word to talk about the weird happenings just before Caesar's death (Julius Caesar, I.iii.28, II.i.198), and Cardinal Pandulph describes people interpreting weather signs in this way: "they will ... call them meteors, prodigies" (King John, III.iv.157). The sense can be personalised, as when Queen Margaret describes Richard III as a "valiant crook-back prodigy" (Henry VI part 3, I.iv.75) meaning "monster, abnormal birth". Petruchio's wedding-attire caused guests to look "As if they sawSome comet, or unusual prodigy" (The Taming of the Shrew III.ii.95).
David Crystal is the author, with Ben Crystal, of Shakespeare's Words, published by Penguin