Primulam

Abstract

A board game incorporating the Ulam Spiral in which players compete to advance along a square spiral path of natural numbers via the prime numbers which are color coded according to the order of the subsequence of primes to which they belong. A player can occupy only one position on the board at any one time, and the player's position is determined by the prime index total that is accumulated via the roll of a die at each turn. The first player to reach the first prime number above some predetermined point on the natural number line wins the game.

What is claimed is: 
     
         1 . A board game comprising:
 a game board that incorporates the Ulam Spiral as the pathway of natural numbers along which a player advances via the prime numbers on the path.   
     
     
         2 . A board game comprising:
 the board game in  claim 1  wherein the prime numbers and/or their associated indexes are enclosed within squares or other shapes that are filled or otherwise marked with a color according to the prime number subsequence to which they belong.   
     
     
         3 . A board game comprising:
 the board game in  claim 2  wherein the prime number subsequences identified by color code on the game board include the inventor's prime number sequences A333242, A333243, and A333244 which are published by the Online Encyclopedia of Integer Sequences.   
     
     
         4 . A board game comprising:
 the board game in  claim 1  which includes a game board positional token for each player that is color coded to identify each individual player and their location on the board.   
     
     
         5 . A board game comprising:
 the board game in  claim 4  which includes a colored die for each player that matches the color of the player's positional token to keep track of which player has rolled a die and which token gets moved.   
     
     
         6 . A board game comprising:
 the board game in  claim 1  which includes a reference chart for each player of all the prime numbers up to 1009 and their associated indexes or sequence within the set of all prime numbers.   
     
     
         7 . A board game comprising:
 the board game in  claim 1  which includes a quick guide of the rules associated with the various allowable moves and restrictions according to the prime number which would be landed upon as determined by the roll of a die.   
     
     
         8 . The name PRIMULAM of the board game in  claim 1 , wherein:
 in one sense, a compound word consisting of “prim-” representing “prime numbers”, and “-ulam” representing the last name of the discoverer of the Ulam Spiral, the mathematician and scientist Stanislaw “Ulam”;   in another sense, “primulam” is the accusative feminine singular of “primulas”, meaning “the very first” in Latin.   
     
     
         9 . A board came comprising:
 the board game in  claim 2  as an educational tool to aid the student in the learning and memorization of the first 169 prime numbers and their associated indexes. Variations of the game board may include omitting either the prime numbers or the indexes of the prime numbers from the colored squares as a challenge to the student to memorize the first 169 prime numbers and their associated indexes.   
     
     
         10 . A board came comprising:
 the board game in  claim 1  which may be modified to configure different strategies, challenges, privileges, or restrictions in order to enhance the game.   
     
     
         11 . A board came comprising:
 the board game in  claim 1  which may include any computerized variations of the game which would increase the entertainment and/or ease of playing the game such as lighted colored squares, sound effects, push button controls, or electronic methods of simulating the process of a random roll of the die and/or the identification of the location of a player on the board.