I've heard base 12 is better, but what about base 30 ?
Learning multiplication tables in another base would be quite fastidious, so I don't know if that already been tried before...
(I don't know what sort of tags I should put on this one)
Asked
Active
Viewed 38 times
2
-
In general there are n(n+1)/2 entries in the multiplication table of base n (because you don't need to memorise ab if you know ba). As paw has answered, this would only help you to find smaller prime factors, and would not be efficient to determine the primality of a number because you'd have to convert between bases which would only complicate matters. – Frank Vel Sep 28 '14 at 13:01
1 Answers
3
I'd try base six, which has instant divisibility tests for divisibility $2$ and $3$ and a sum-of-digits tests for divisibility by $5$, and an alternating sum of digits test for divisibility by $7$. Also its multiplication table has only $36$ entries. (Your idea of base thirty has instant tests for $2, 3, 5$ and sum/alternating sum tests for $29, 31$. But in base thirty your multiplication table has $900$ entries to learn.)
To be honest though, the heart of (hard) primality testing has to do with finding large prime factors, and I don't see any base helping much with that.
paw88789
- 40,402
-
1+1 for the second paragraph. Finding small prime factors is easy in any base. – Charles Sep 29 '14 at 14:02