Is the mate-in-n problem of infinite chess with each color using traditional pieces plus one huygens decidable? I noticed in a paper that the mate-in-n problem of chess, even played on an infinite board is decidable. The mate-in-n problem of inﬁnite chess is decidable

I believe the paper assumes only traditional chess pieces are used.

What if one of the chess pieces is a huygens? (A huygens is a chess piece which jumps prime numbers of squares).

Is the mate-in-n problem of chess on an unbounded board with each color using traditional chess pieces plus at least one huygens also decidable?
Presburger arithmetic with a predicate for the primes is probably undecidable, so at least the technique used by your question's link should not easily generalize to allowing a huygens.

For example, although decidability of the special case I'm about to mention

would follow from there being only finitely many positive even integers that

are neither prime gaps nor sums of two distinct primes, I don't see any way of

proving decidability of mate-in-ONE for king+huygens against a smothered king: