Mate in N. What is the largest N known? 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?
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.

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