On the 23rd of Christmas, my true love gave to me: 23 prime rectangles…
I disagree, unless we have a very different definition of the term ‘shape’. There are many shapes that, while regular, do not involve components of equal size and thus might happen to be made up with numbers that are prime. The first one that occurs to me are the shapes of regular hexagons made up out of closely packed circles or miniature hexagons.
Aside from a single element, the next hexagon is made up of seven elements - one in the middle and six surrounding it. Seven is, of course, a prime number. Then the next biggest involves laying twelve further elements in another ‘ring’ outside, six at the points and six more in between the points, for a total of 19 as the third hexagonal number. (Also prime.)
Working out the first 30 hexagonal numbers and doing my best to factor them, I get the following results:
1 Neither
7 Prime
19 Prime
37 Prime
61 Prime
91 7 * 13
127 Prime
169 13 * 13
217 7 * 31
271 Prime
331 Prime
397 Prime
469 7 * 67
547 Prime
631 Prime
721 7 * 103
817 19 * 43
919 Prime
1027 13 * 79
1141 7 * 163
1261 13 * 97
1387 19 * 73
1519 7 * 7 * 31
1657 Prime
1801 Prime
1951 Prime
2107 7 * 7 * 43
2269 Prime
2437 Prime
2611 7 * 373
That’s 16 primes, 13 composites, and 1 neither. Not too bad a record. (Of course, it’s the 1 in the center that keeps the sequence from being always a multiple of six, but that is the way that this particular pattern works.)
Is that like… a golf ball or soccer ball? The joining of various shapes to make a whole new overall shape?
I think we were defining shape differently, and I was also making the implicit assumption that every example in the series had to be prime. If not, then you can always find some pleasing arrangement of a large number of individual pieces that can be called a shape.
Otherwise you can do it even in two dimensions just by adding primes.
1
1,2 = 3
1,2,3
1,2,3,5 = 11
1,2,3,5,7
1,2,3,5,7,11 = 29
etc.
I wasn’t meaning to imply that there was any series of shapes that was ALWAYS made up by a prime number. That would pretty much mean it made a prime generation algorithm.
Thee Temple of Psychick Youth says
It seems that a lot of their ideology is based on 23, though…
Genesis P. Orridge was a bit of a kook when he started it…and s/he still is…