Boxy Numbers

16 Apr 2008

My previous post “Basic Primes in Scala” ended with some ideas of how to salvage some use out of the algorithm. I mentioned representing the numbers as concentric circles. Playing around with a text editor, I converted some of the numbers to arrangements of concentric squares.

Left to right are the factors, rearrange at will. The vertical arrangement represents the power.

Here are some of the results shown in the previously generated style, and recreated as groups of concentric squares.

2:[]

[]

3:[[]]
 ____
[    ]
[ [] ]
[____]

4:[]([])

[]

[]

5:[[[]]]
 ________
[  ____  ]
[ [    ] ]
[ [ [] ] ]
[ [____] ]
[________]

6:[[]][]
 ____
[    ]
[ [] ]
[____] []

7:[[]([])]
 ____
[    ]
[ [] ]
[    ]
[ [] ]
[____]

8:[]([[]])
 ____
[    ]
[ [] ]
[____]

[]

9:[[]]([])

[]
 ____
[    ]
[ [] ]
[____]

10:[[[]]][]
 ________
[  ____  ]
[ [    ] ]
[ [ [] ] ]
[ [____] ]
[________] []

11:[[[[]]]]
 ____________
[  ________  ]
[ [  ____  ] ]
[ [ [    ] ] ]
[ [ [ [] ] ] ]
[ [ [____] ] ]
[ [________] ]
[____________]

...

293:[[[[[[]]]]][]]
 _______________________
[  ________________     ]
[ [  ____________  ]    ]
[ [ [  ________  ] ]    ]
[ [ [ [  ____  ] ] ]    ]
[ [ [ [ [    ] ] ] ]    ]
[ [ [ [ [ [] ] ] ] ]    ]
[ [ [ [ [____] ] ] ]    ]
[ [ [ [________] ] ]    ]
[ [ [____________] ]    ]
[ [________________] [] ]
[_______________________]

294:[[]([])]([])[[]][]

[]
 ____
[    ]
[ [] ]  ____
[    ] [    ]
[ [] ] [ [] ]
[____] [____] []

295:[[[[]([])]]][[[]]]
 ____________
[  ________  ]
[ [  ____  ] ]
[ [ [    ] ] ]
[ [ [ [] ] ] ]  ________
[ [ [    ] ] ] [  ____  ]
[ [ [ [] ] ] ] [ [    ] ]
[ [ [____] ] ] [ [ [] ] ]
[ [________] ] [ [____] ]
[____________] [________]

296:[[[]][]([])][]([[]])
 ___________   ____
[  ____     ] [    ]
[ [    ] [] ] [ [] ]
[ [ [] ]    ] [____]
[ [____] [] ]
[___________] []

297:[[[[]]]][[]]([[]])
 ____________   ____
[  ________  ] [    ]
[ [  ____  ] ] [ [] ]
[ [ [    ] ] ] [____]
[ [ [ [] ] ] ]  ____
[ [ [____] ] ] [    ]
[ [________] ] [ [] ]
[____________] [____]

298:[[[]([])][[[]]]][]
 ___________________
[  ____   ________  ]
[ [    ] [  ____  ] ]
[ [ [] ] [ [    ] ] ]
[ [    ] [ [ [] ] ] ]
[ [ [] ] [ [____] ] ]
[ [____] [________] ]
[___________________] []

299:[[[]]([])][[[]][]]
 ________
[        ]
[  []    ]  ___________
[  ____  ] [  ____     ]
[ [    ] ] [ [    ]    ]
[ [ [] ] ] [ [ [] ]    ]
[ [____] ] [ [____] [] ]
[________] [___________]

300:[[[]]]([])[[]][]([])

[]
 ________
[  ____  ]
[ [    ] ]  ____
[ [ [] ] ] [    ] []
[ [____] ] [ [] ]
[________] [____] []

One of the IP addresses of this blog: 72.233.2.56:

 ______________________   ____________
[                      ] [  ________  ]
[ []                   ] [ [  ____  ] ]                ____________
[  ________            ] [ [ [    ] ] ]               [  ________  ]
[ [  ____  ]           ] [ [ [ [] ] ] ]  ___________  [ [  ____  ] ]  ____          ____
[ [ [    ] ]  ____     ] [ [ [    ] ] ] [  ____     ] [ [ [    ] ] ] [    ]        [    ]
[ [ [ [] ] ] [    ]    ] [ [ [ [] ] ] ] [ [    ]    ] [ [ [ [] ] ] ] [ [] ]  ____  [ [] ]
[ [ [____] ] [ [] ]    ] [ [ [____] ] ] [ [ [] ]    ] [ [ [____] ] ] [    ] [    ] [____]
[ [________] [____] [] ] [ [________] ] [ [____] [] ] [ [________] ] [ [] ] [ [] ]
[______________________] [____________] [___________] [____________] [____] [____] []

Explanation: The IP 72.233.2.56 = 1223230008

1223230008 = 863 * 59 * 13 * 11 * 7 * 3 * 2^3

863 is the 150th prime. 150 = 5^2 * 3 * 2

59 is the 17th prime. 17 is the 7th prime.

13 is the 6th prime.