Squares of primes
The squares of primes (except 22 and 32) are all on the same radius of the number circle.
Explanation
There are three types of natural numbers. Except the 0 they can all be derived.
3 × 3 6 9 12 15 18 21 24 27 30 33 36 39 ... 2 × 2 4 8 10 14 16 20 22 26 28 32 34 38 ... rest 1 5 7 11 13 17 19 23 25 29 31 35 37 ...
The squares on the bottom row are on the ray that starts with the number 1.
Squares i2 12 52 72 112 132 172 192 232 252 292 312 352 372 ... Vakue −1 1 25 49 121 169 289 361 529 625 841 961 1225 1369 ...
The distances between the squares can be split in two strokes. The 4-stroke 12 → 52, 72 → 112, 132 → 172, 192 → 232 delivers the distances 0, 2, 4, 6, 8, ... and the 2-stroke i2 → 12, 52 → 72, 112 → 132, 172 → 192 delivers the distances ø, 0, 1, 2, 3, 4, ... This sequence also appears in the repeating fraction
The development of these two strokes can be shown in a single radius of the prime number cross.
Peel 4-s Ray 2-s 42 985 41 312 →4 40 937 39 913 38 889 37 865 36 8← 292 35 817 34 793 33 769 32 745 31 721 30 697 29 673 28 649 27 252 →3 26 601 25 577 24 553 23 6← 232 22 505 21 481 20 457 19 433 18 409 17 385 16 192 →2 15 337 14 313 13 4← 172 12 265 11 241 10 217 9 193 8 132 →1 7 145 6 2← 112 5 97 4 73 3 72 →0 2 0← 52 1 12 →ø 0 i2
The imaginary unit is defined as i 2 = –1 and is located on the unit circle. It is a mirror image of the number +1.