gwnn, on 2012-October-18, 04:56, said:
If you square any prime number (greater than 3) and subtract 1, you get a number divisible by 24.
24 divides n2-1 if and only if n is not divisible by 2 or 3. Perhaps your observation is deeper than it appears, though, since when movement manuals talk about needing a "prime number" it is actually sufficient to use a number which isn't divisible by 2 or 3 (such as for rainbow movements, which work perfectly well with 25 tables should you be lucky enough to find 100 people who like individuals).