If I want to learn to count in another base to calculate primality, which one should I try?

Question

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)

Answer 1

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.