Why not any prime number from 5 on?

# Chess on an Infinite Plane - Huygens Option

**any**prime number of squares (5 or more) like EvertVB suggested. So that's 5, 7, 11, 13, 17, 19, 23, 29, 31...etc. All other rules are the same as listed above. I'll play:

**1...c5 (3,5)**

If the Huygens can jump any number of squares, can't they take each other immediately? There are 19 squares between them...

The Huygens jump **prime numbers** of squares (starting 5 or more). And prime numbers are a little weird - they don't have any normal repeating pattern. I have a list of all prime numbers from 5 to 499. Here they are:

5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499.

The pieces 19 squares apart are the Hawks, not the Huygens. Hawks only make jumps of 2 or 3 squares. The Huygens are the pieces that look like they have antenna on their heads. There's nothing they can attack on their first move.

Background: The rules for "Chess on an Infinite Plane" were completed January 16.(Link here).Formation Chess" was blended with the infinite plane. The bishops and chancellors were disbanded and replaced with an army of knights - fourteen for each color. The knights can cluster into formations, and thereby able to rapidly travel as queen to other areas of the board. (Link here).Chess on an Infinite Plane - Huygens Option". In this variation, two huygens are added to each army.Huygens can jump 5, 7, 11, or 13 squares in orthogonal directions. These are prime numbers, so when fleeing from another jumper (such as a hawk), the pursuer needs to make an inefficient maneuver to capture the Huygens, causing wasted moves.

Rules:The Pieces:Black and White each have the following pieces (quantity and name):

1 queen

2 chancellors

2 rooks

2 bishops

2 knights

2 guards

2 hawks

2 huygens

22 pawns

Chancellor(C) - Moves and captures as rook + knight.Hawk(Ha) - Leaps exactly 2 or 3 squares in any orthogonal or diagonal direction. The leaping move means it can jump over other pieces.Guard(G) - Moves and captures the same as a king but is not affected by check. Other information on the guard can be found (here). (not particular to this game)Huygens(Hu) - Leaps 5, 7, 11, or 13 squares in any orthogonal direction.Pawns play the same and promote at the same rank as in classical chess. White pawns promote at rank 8, and black pawns promote at rank 1. Pawns can promote to chancellor, hawk, huygens, or guard in addition to queen, rook, bishop, or knight. Pawns may capture en passant with the same rules as in classical chess.

Board Setup:A red bracket indicates the a1 (1,1) square.

There is no castling.There is no fifty-move rule.Draws can only occur from stalemate, threefold repetition, agreement, or a proven case of insufficient material to force checkmate.The Chessboard:1. Board for OTB Play:

A playing area should be setup with at least 22 ranks and 20 files. Ensure provisions are available to expand the board if play requires. If this becomes inconvenient due to far-away pieces, a display board is used to indicate the location of remote pieces. If there is interesting play in small but remote areas, other playing areas can be labeled and used separatelly from the main board.

2. Diagram for Online Play:

A chess diagram is used to indicate the position of pieces either after each move by white, or each move by black. The diagram should include 22 ranks and 20 files. If any pieces are moved outside of this area, the diagram is expanded or notes are shared to indicate the location of far-away pieces. If there is interesting play in small but remote areas, other diagrams can be used to show piece positions separatelly from the main diagram.

Move Notation:Numeric coordinates are used to identify piece locations as (file#, rank#). The "a1" square is (1,1) and is marked on the chess diagram with a small red bracket. Increasing files are to the right, and increasing ranks are toward the back.

Parenthesis are used around each coordinate. Three examples of a move notation:

1) A rook moving from (8,4) to (1,4):

R(8,4)-(1,4) or R(1,4)

2) A rook moving from (1,4) and capturing a piece on (0,4):

R(1,4)x(0,4) or Rx(0,4)

3) A pawn advancing from (-1,7) to (-1,6):

(-1,7)-(-1,6) or (-1,6)