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What known position has one side with a forced mate in N moves, with N the largest? I came across one with 517 moves using only 7 pieces, so there should be much be larger. (Ignoring the 50-move rule).

Dont know if this is on-topic here, - but how large can we make N (asymptotically) on an nxn chess-board with any number of pieces and placements?

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I think answers to this question fall into 2 categories : problem composition and computer-driven few-pieced endgames' thorough analysis. The second one — to which your discovery belongs — being a tad bit more efficient than the first, that's probably all there is to say about it, if you're about sheer numbers. Art still has a long way to go on this road.

Regarding computer-driven endgames, the longest known so far is 549 moves long.

[FEN "1n1k4/6Q1/5KP1/8/7b/1r6/8/8 w - - 0 1"]
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