="Dan Asimov" <dasimov@earthlink.net> My favorite number is 24 hands down, because of its amazing properties like showing up in [...]
It's interesting how diverse people's esthetics can be. I find 24 pleasant for all the reasons cited, but feel this ubiquity and regularity make it a bit too stolid and boring. Perhaps I'm too inclined to novelty, but when an answer turns out to be a number like 24 it's like learning that breakfast is a bowl of cornflakes and skim milk. In contrast, I tend to prefer eruptions of unexpected unique identity against an apparently uniform background--like a frog leaping out of a bowl of curry! So my "canonical" favorite number is 691.
But how about prime numbers? After the first few, how do you distinguish, say, 101, 103, 107, 109 ?
I like Ramanujan's famous exhortation to "make friends with the integers", and tend to view unfamiliar numbers as friends I haven't yet made, but can look forward to getting to know better, should the opportunity arise. I find it particularly ironic that this list ends with 109, which lately to me is an attention-grabbing SETI signal that's associated with some topics of personal interest! See for example the thread on math-fun from last November with subject "Coincidentally 109", and OEIS sequence A054244 and others related to (binary) "dismal arithmetic".
Are there standard measures of some sort that distinguish among prime numbers?
That's an interesting idea. I prefer primes that aren't tweaks of vanilla "round" numbers. By that standard I find 17 to be much less cool than 19. It's not at all clear, though, how to quantify that. Intuitively, there might be some kind of complexity measure, such as the simplest/shortest recurrence that generates N (say using just 1, addition and functional composition)?