"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.