Enter Your Reply The Comment You're Replying To V. Reinhart wrote on Fri, Feb 24, 2017 12:05 AM UTC:The Huygens Chess Piece The huygens is a chess piece that jumps in a rook's direction any prime number of squares (2, 3, 5, 7, 11, 13, 17, 19, 23,...). I use it in the chess variant Trappist-1. "H" - Huygens In some games it may be limited to a minimum jump so that it is not a close attacker. The following are my estimates of the huygens' value based on its minimum jump: Allowed Jumps - Estimated Piece Value: 2, 3, 5, 7, 11...(value = rook + 2 pawns) 3, 5, 7, 11... (value = rook+) 5, 7, 11... (value = bishop+) There are an infinite number of prime numbers, so in theory a huygens can jump infinitely far. However, not all prime numbers are known. The largest known prime number is [2^(74,207,281) − 1] (which has 22,338,618 digits). Although a huygens can jump infinitely far, when playing chess, the players must declare the specific square that a piece is to be moved to. So this limits the distance that a huygens can travel in a single move. It is the player that moves the huygens that carries the burden to prove that a number is prime. (If his opponent requests it, he would need to cite the source showing the leaping distance is a prime number). An example of a large legal move would be: Hb[(2,996,863,034,895 x 2^(1,290,000) + 1], Chris K. Caldwell. "The Top Twenty Twin Primes" In an actual game there would not normally be any reason to move a piece this far, because then it would lose its targets, and especially its ability to create forks in different directions. But I think it's good to make sure all the rules of a game and its pieces are carefully defined, so there will be no questions or points of contention once a game starts. The huygens (white) is shown in the diagram below on square b2, and its moves are indicated with red symbols. This diagram is a 50x50 grid, but when played in Chess on an Infinite Plane, the huygens can jump to numerous other squares outside the boundary of this diagram. A link to Trappist-1 is here: Trappist-1 Edit Form Subject: Name or UserID: Password: if signing in with UserIDComment or question: Format: HTMLMarkdownTextWYSIWYG Conduct Guidelines This is a Chess variants website, not a general forum. Please limit your comments to Chess variants or the operation of this site. Keep this website a safe space for Chess variant hobbyists of all stripes. Because we want people to feel comfortable here no matter what their political or religious beliefs might be, we ask you to avoid discussing politics, religion, or other controversial subjects here. No matter how passionately you feel about any of these subjects, just take it someplace else. Avoid Inflammatory Comments If you are feeling anger, keep it to yourself until you calm down. 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