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Any good ideas for mystical numbers?

Ry

Retired User
A setting I'm making needs a special number for its calendar, and I've been bouncing between a few but I thought you guys might have suggestions.

I'm looking for a number, hopefully larger than 100, and either a coprime with 120 or having an other obscure relationship with it.

Mystical patterns that have X many elements, reasons the number is intrinsically beautiful, and so on, are all very welcome.
 

s/LaSH

Member
RPGnet Member
Validated User
I'm no numerologist, and it's not coprime, but 360 is a great number because of all its possible factors, some of which are bound to be mystically significant (it doesn't have 7, but it does have 40). And it's almost the length of the year, so ancient civilisations are fond of making it the actual length of the year and then having some intercalary days that aren't proper days so their midwinter feasts don't drift into spring a few decades down the line, which are great periods for supernatural wackiness - not part of a year, so all manner of things crawl out of the woodwork.
 

Ry

Retired User
Well, 120 is multiply-perfect, superabundant, highly composite, a triangular, tetrahedral, and hexagonal number, the sum of a twin prime pair, the sum of four consecutive primes, four consecutive powers of two, four consecutive powers of three, and so on. It's the lowest number to have 16 factors, so the factors thing I've got down.

In what I'm working on there are precisely 12 months in a year, and so 120 months = 1 decade. Each month of the decade has a different name.

I'm sort of looking for something with a different vibe when it comes to the coprime number.
 

S.K.

I should know better.
Well, if you want something as dissimilar from 120 as possible...

133<sub>10</sub> = 250<sub>7</sub> = 2<sup>3</sup> + 5<sup>3</sup> + 0<sup>3</sup> (a base-7 narcissistic number)? It's also 7 · 19, so it's a semiprime (a prime would be too obvious, I think).

If you really want representation-independent properties, 1001 springs to mind: just offhand, it's the sum of two cubes and the product of three consecutive primes. In base 30 it's (33,11).

210, although decidedly not coprime, is possibly nice: 120 = 5!, 210 = 7#.

There's also 377, solely on the grounds that 377/120 is close to π. (Not nearly as close as 355/113, of course, but what can you do? ... well, you can wrap a 100-sequence around it and make the 100th 377-cycle a 376-cycle, I guess.) It's also a semiprime: 13 · 29.
 

Ry

Retired User
Awesome; S.K. I'm going to use 120*pi for my solar cycle.

That gives pi days per "card"; a deck of cards in the setting has 120 elements.

Looking at semiprimes, I think 1261 = 13 * 97 is kind of fancy; one of the cool properties that 120 lacks is being a star number. 121 is also a star number (and a chinese checkers board) so that's kind of fancy, but makes me wonder if I'm shaving it too close (so to speak).
 
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