Springing from the discussion on Ark's blog, here's some fun with prime numbers.
For starters, using Wolfram's Mathematica's function Prime[n], which returns n-th member of the infinite set of prime numbers, a 10×10 table of prime numbers looks like this:
PrimeTable10 = Partition[Table[Prime[n], {n, 100}], 10] // TableForm ;
{ {2, 3, 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, 503, 509, 521, 523, 541}}.
It looks easier to read if transported from Mathematica as a PNG file, instead of just copy-pasting:
View attachment 100413.
Things started to look interesting when additional properties of being a prime number were taken into account, which ultimately produced the PrimeGrid (explained below). Using Mathematica, one possibility of creating this grid of prime numbers, the dwellings of the mystics, would be:
Priming[n_, k_] := NestList[ Prime, Prime[n], k - 1];
PrimeGrid[n_] := Partition[ Flatten[ Table[ Priming[i, j], {i, n}, {j, {n}} ]], n].
Here's how PrimeGrid(7) looks like in Mathematica:
View attachment 100414.
It looks easier to read when inverted upside down, so that prime numbers lower in order are below those of higher order, in addition to adding natural numbers as their origins below the first row of such a table. Unfortunately, the Table option on the Forum appears to be too consuming to do that here and now, so without further ado below is PrimeGrid(12) as obtained by Mathematica, i.e. 12×12 array or grid of prime numbers with additional qualities of being a prime number.
View attachment 100415
Tridimensionality can be visualized for starters, with the plane of natural numbers below and additional planes of the above grid, starting with the row corresponding to how high you go, above the plane/grid shown here above.
In short, first row from above are the prime numbers, going as far as you like and know them. Next row is obtained by applying the number values, those of being a prime number, to the residing row. In practice, 1st prime number is 2 and on the second place in 1st row is 3, 2nd prime number in order, and so 3 becomes first member of 2nd row. It continues like this all the way from the first column on the left. For the next row, you apply the same procedure. First prime number is 2, on the 2nd place in 2nd row is 5, being 3rd prime in order as 3 stands on the 2nd place in the prime number set.