This is a linkpost for https://pabloernesto.github.io/2022/01/17/dndsci-2-2.html
You asked what Guy and I were looking for that led us to notice the prime-factors thing. In my case, the answer is just that by training I'm a pure mathematician and I can't help noticing that sort of thing. For whatever reason it didn't occur to me to, e.g., look at the distributions of the exponents of 2, 3, and 5 or anything like that, not that doing so would have led me to pick different items or anything.
(I was glad to see that you liked "Wakalix Maketh it Goe".)
Thank you gjm and Guy for the responses! It lifts my spirits immensely to know that my work is being received favorably.
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These write-ups are fantastic! Keep 'em up: selfishly, so that I can keep reading them! :D
IIRC, the reason I was looking at prime factors was because I noticed the multiplicity of certain large values was high when collecting all the high value items to see if I saw patterns, then noticing that the values which actually appeared rather than those which never appeared seemed to have an unusually high number of small factors.
I see. The spikiness is a tipoff that the numbers are being generated by some simple underlying process. I'm still not clear about why primes, though.
I'm guessing the idea is looking out for multiplicative processes, like looking out for the hump-tail shape of the distribution? Multiplying numbers together is an addition on their multiplicities-of-factors representation, so nd6 can never generate a number with a prime factor of 7 or higher. But I'm not explicitly hearing that as the rationale, so it feels like "primes are bound to show up, just keep an eye out for them".
Oh. Um, I just see a lot of numbers as their prime factorization so it was obvious something unusual was going on. Probably not helpful to you, there. But I guess it's similar to what gjm said. Like how you'd notice if everything was divisible by 10 because everything ended in 0s, but not quite so clear.
Maybe it is. Feynman's abacus story suggests that he (and colleagues) were familiar with lots of specific numbers and that it matters, somehow. Perhaps I should pick up the habit. Or perhaps that's backwards, and there's some particularly useful skill tree that, as a side effect, results in learning to recognize lots of numbers. Either way, just knowing that this is a common thing among the mathematically inclined is worth knowing.
If I had to guess, I'd guess that the largest contributor towards viewing numbers like that was probably my courses taught from https://www.amazon.com/Discrete-Combinatorial-Mathematics-Applied-Introduction/dp/0201199122/ in university.
Thank you gjm and Guy for the responses! It lifts my spirits immensely to know that my work is being received favorably.
Reproduced verbatim so both recipients are notified.