paperbackwriter you are exactly right about Cabral’s voyage. You are also correct in that you did ultimately say “across the North Atlantic” to here. But you did open with the statement,
"I’m not expert on this by any means, but I think the supposition that random storms would blow unlucky European or Near Eastern mariners to North American is unlikely."
Doesn’t suggest that the South Atlantic was off limits to Europeans. I do agree it is very unlikely they were “blown” across the North Atlantic. But according to my dad, (old navy man from WW2 and Korea) “It might not blow you across, but it’ll force you to cross. Either that or it’ll drown you.”
He did NOT like the North Atlantic from what I gather.
BrainGlutton Yeah, I was just saying that Easter Island is a hell of a long way, even from it’s closest neighbor. AFAIK they could’ve gotten blown to Chili first, then in an attempt to get back home wound up stranded on the island. In any event, it’s not likely they were native. The point was that people have discovered “unknown” lands by accident.
So, whatever became of the two Roman shipwrecks found in the Caribbean. I think one was 2nd century off the coast of Brazil and the other was 3rd century found off the coast in Central America? (Maybe off the Yucatan Peninsula) Could be a crock <heh> for all I know. The Smithsonian supposedly has some relics as does the Brazilian government.
I’ve studied maps, currents, depths of land masses underwater, existing islands, changing ocean levels (specifically the Atlantic) at various times in man’s history. If the world’s oceans have risen (some say as much as four hundred feet in the past few thousand years) let’s just say a couple of hundred feet, there would have been at least four or five major islands between Brazil and Africa. Some of these masses can be found even now at certain times of the year. There are also several points where the water is very shallow (25-50’) When these points were above water, some as recent as 200-300 years ago. That’s only a few hundred miles in between islands. They run in a fairly straight line as well. Between the erosion and rising sea levels these old islands (save a couple) are no longer present. I don’t think it’d be that hard to cross under these conditions. Just watch out for the hurricanes. 
Finally, I’m not quoting Heyderdahl…but AFAIK it’s commonly accepted that the Irish monks were persecuted and did flee in advance of the Vikings. Whether they made it as far as North America is questionable.
BTW I’ve been reading a highschool history textbook by coincidence this week. In it this OP is actually addressed and the text presents both sides of the issue. It makes reference to claims that Columbus wasn’t the first (besides Norsemen) <ahem> It claims Columbus knew where he was going and perhaps even had maps, “directions”, evidence or some knowledge left by others before him. It definitely leaves the possibility open for debate.
