Are premonitions and prophetic dreams real?

I think the question itself is formulated a bit wrong. Premonitions and prophetic dreams are different things, and while the former can at least be explained through the subconscious, the latter already border on mysticism. I'm a skeptic, but I'll note this: over seven years I've observed how people often confuse coincidences with predictions. I remember once forgetting about some dream long ago, and then something happened - and immediately I remembered that dream and decided it had been "prophetic." The brain works in such a way that it first searches for coincidences, and then rewrites the story after the fact.

As for premonitions, I agree with what the person above wrote - it really can be the work of the subconscious. It absorbs tons of information: a person's intonation, their posture, body language, certain smells or sounds. Consciousness hasn't processed it, but the body's already reacting - pulse quickens, hair stands on end. Later we call this a premonition, but really we just skipped the intermediate stages of analysis. That's all there is to it.

And prophetic dreams - that's more a matter of statistics. We see hundreds of dreams in our lifetime, and of course about 10 percent of them will coincide with real events one way or another just by the law of large numbers. But we only remember the ones that came true and forget the rest.