>>6177
I'm seeing the pattern, and it seems to pop up a lot–mostly when you multiply
two consecutive primes, but there are other instances.
Let's take a look at the consecutive ones:
1 * 2 = 2; 0 in either direction
2 * 3 = 12; 4 cw from 2, or 3 cw from 3
3 * 5 = 15; 10 cw from 5 (the larger)
5 * 7 = 35; 10 ccw from 5 (the smaller)
7 * 11 = 77; 10 ccw from 7 (the smaller)
11 * 13 = 143 10 cw from 13 (the larger)
13 * 17 = 221 10 cw from 11 (the smaller)
17 * 19 = 323 14 ccw from 17, 16 ccw from 19 //breakdown
19 * 23 = 437 22 ccw from 19, 14 cw from 23 //breakdown
23 * 29 = 667 4 cw from 23, 2 ccw from 29 //breakdown
29 * 31 = 899 10 ccw from 29 (the smaller)
31 * 37 = 1147 10 ccw from 37 (the larger)
With one prime between:
1 * 3 = 3 0 and 2
2 * 5 = 10 8 and 5
3 * 7 = 21 18 and 14
5 * 11 = 55 10 cw from 5 (the smaller))
7 * 13 = 91 4 and 2
11 * 17 = 187 10 cw from 17 (the larger)
13 * 19 = 247 5 and 12
17 * 23 = 391 14 and 8
with two primes between (skipping the lower ones)
3 * 11 = 33 10 ccw from 3 (the smaller)
5 * 13 = 65 20 and 12
7 * 17 = 119 8 and 18
11 * 19 = 209 10 ccw from 19 (the larger)
13 * 23 = 299 6 and 4
17 * 29 = 493 14 and 14
19 * 31 = 589 10 cw from 19 (the smaller)
23 * 37 = 851 12 and 14
…so what you mention pops up a lot more often that one would expect, but it
doesn't hold in every situation. It's interesting that in a lot of cases, the
offset from each factor either adds to, or is the difference of, the difference
between the two primes. I would say that it's also interesting that the
difference between the rays is always an even number, but that's made pretty
plain by the diagram.