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I enjoy variants whose only point is to explore some weird idea, but I don't think this brings enough to the table to publish. Only rooks and queens can cross the board (without adding some rules for facilitating automatic advancement of other pieces) and will get slaughtered by the opponent's remaining army.

I think I've seen a similar variant where the space between armies is actually infinite, but I can't immediately find it, and I don't know if there was a serious attempt at making it playable?

Since large primes are all odd, you're guaranteed to need an additional row to get the square coloring you're after.