Impossible-to-reach position with the least amount of pieces?

It's very easy to setup a position in chess that's completely legal (eg. no pawns on the first or eighth ranks, there are only two kings of opposite colors and both kings are not in check at the same time, etc.) but which is impossible to reach via legal moves from the standard starting positions. For example, take the starting position and just swap the king and the queen, for example.

However, I was wondering what would be the minimum amount of pieces for such an impossible-to-reach position?

I'm thinking that there may be some positions with just like 4 or 5 pieces on the board which is legal itself, but impossible to reach from the standard starting position via legal moves only.

(And in the spirit of the problem, I don't consider putting 9 pawns of the same color,or more of a particular piece than could be achieved by promoting all 8 pawns to it, a valid solution. That would be too trivial, and too boring, of a "solution".)

True. I didn't think of such a situation with a bishop behind a pawn like that.

for some reason this position exists in the syzygy tablebase https://syzygy-tables.info/?fen=8/1k6/8/8/8/6P1/8/1K5B_b_-_-_0_1

Wow that's actually pretty cool!

OP asks for illegal positions.

OP said only that both kings shouldn't be in check, not that the side not to move shouldn't be in check. 

This is one with 5 moves, but it's still illegal because the 2 pawns are blocking the bishop's exits, so technically it couldn't have moved.

In a similar way:

If you notice carefully, the 3rd rank is entirely guarded by the pawns, so technically the king should not be able to get to the 1st rank.

in the 1st one white could have underpromoted to a dark bishop so it is still legal

This does it with 2.

This explains

http://anselan.com/tutorial.html

By "legal position" people generally mean one that can be reached from the starting position according to the rules, either at the point where a move has been made or the starting position itself. With that understanding, what you say is very easy in your first paragraph is not actually possible and your example with queen and king swapped is not at all completely legal.

You obviously mean something different by "legal position" and in that case the examples of positional attributes that render a position illegal according to your understanding (the bracketed clause) needs to be made explicit and complete if the question is to be well defined.

No it's not.

In your first example, the position after White's move 2 is dead (no legal play can result in mate), so the game is terminated at that point. Black doesn't get a move 2. (Your chess program lets Black play move 2 because it doesn't know how to check if a position is dead, but the move and the resulting position are no longer part of a game. A human arbiter should declare the game drawn before the position I showed is reached.)

Your second example is OK because the game is not dead until after White's move 2. (He could have played 2.Ke5 after which it's possible for Black to mate.) Unfortunately the resulting position is Black to move, not, as specified, White to move.

Buchanan's position with White to move cannot be reached in a legitimate game.

Many such things slip under the net. E.g. the last ply in this game shouldn't be there because the position was already dead (no way to checkmate within the mandatory 75 move rule)

https://www.chessgames.com/perl/chessgame?gid=1825274

but these are errors and therefore irrelevant to whether or not positions are legal. You could take the queen, but it wouldn't be taken within the game. Of course you should call it a draw. You don't need the arbiter (indeed you may not have one).

Even this (pay attention to the whole board).

Well, given your name is "PromotionZone", I'm pretty certain you know that the bishop can be promoted.

Wow, this is mind boggling. I never thought of the position that deeply.

Here's a quick construction problem with 2 parts.

Part (a): Shift the WHITE king to another square and add one WHITE piece (not a pawn) to create an illegal position. 1 solution.

Part (b): Shift the BLACK king to another square and add one BLACK piece (not a pawn) to create an illegal position. 2 solutions.

Adjacent kings not allowed!

King to b1 and rook on a1 for the first one.

@JustARandomPatzer. Right idea but not quite!