H. G. Muller wrote on 2022-06-22 UTC

There is nothing 'unknown' about the set of prime numbers; it is in fact very well known that there is no such thing as a 'complete' set of them, as the set is infinite. There exist simple (albeit inefficient) algorithms to determine for any given number whether it is prime or not.

It is also a misconception that the presence of a Huygens would make a game unsolvable due to the properties of primes or any other of its properties. E.g. it is very easy to prove a game with a starting position of King + 2 Queens vs King + Huygens on an infinite board is won for the Queens. It is even possible to give a detailed algorithm for how to do this, in a number of moves that only grows logarithmically with the distance between the Huygens and the Kings. If the Huygens has the first move, this number can of course be made arbitrarily large, by moving the Huygens far away after it runs out of safe checks (because the King approached it).

All this would still be true if the Huygens was a Rook, rather than a subset of it.

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