Heads up this whole webpage was written in seximal because I'm tired
Base six times eleven, or nif fifsy, is a decent base. And, with using seximal with it, it becomes usable and even better. Let's start with the why: I discovered this base when trying to think of a way to solve seximal's problem with 15 (eleven). Seximal does not handle elevens well. My first thought was "just multiply the base by eleven lol", and weirdly enough, that actually wasn't terrible. The reason why is that 145 (one less than the base) is divisibile by 5 and 21 (thirteen).
This base is basically seximal but with 15 and 21, and missing 11 (seven). Yeah, other than the size, the biggest flaw is that it doesn't handle sevens.
Let's get into the how. This will of course use mixed radix, so up until 150 this is exactly like seximal. But once you hit 150, you write 1:000 instead.
144
145
1:000
1:001
For large bases, I owe it to baseconvert for making it possible to study. This table was only possible to create because of their website. It's very decimal centric and I don't like the starting set of bases, and it doesn't let you use fractions, but other than that it's perfect. You should be able to change what base is used for the mixed radix of bases greater than niftimal.
| Fraction | Seximal | Hexelevenary |
| 1/2 | 0.3 | 0.53 |
| 1/3 | 0.2 | 0.34 |
| 1/4 | 0.13 | 0.24:53 |
| 1/5 | 0.'1 | 0.'21 |
| 1/10 | 0.1 | 0.21 |
| 1/11 | 0.'05 | 0.'13:44:30:131:101:115 |
| 1/12 | 0.043 | 0.12:24:53 |
| 1/13 | 0.04 | 0.11:34 |
| 1/14 | 0.0'3 | 0.10:'103 |
| 1/15 | 0.'0313452421 | 0.10 |
| 1/20 | 0.03 | 0.5:53 |
| 1/21 | 0.'024340531215 | 0.'5 |
It's pretty clear that hexelevenary is great with large primes, but it's also clear that it sucks at sevenths. Obviously mixed radix big bases are really hard to use, so I don't recommend using this over seximal, but I thought it was interesting that it was so good.
For numbers less than 150, the divisibility tests are all the same. After 150, it's still pretty similar. To test divisibility by 5, add up all the digits, so like 1:004, 1+4 is 5, so it's divisible by 5. This is also how you check for divisibility by dozen one. For example, 2:015, 2+15 is 21, so the whole number is divisible by 21. Usually last digit divisibility tests suck for large bases, but in this case there are only six multiples of eleven so it's not too bad. If a number ends in 000, 015, 034, 053, 112 or 131, the number is divisible by 15.
We lose seven, as stated earlier, but also as a large base, we lose powers of the base. There isn't a good divisibility test for 4. Or nine, twelve, etc. (Except for numbers under 150, but that's been mentioned before.)
Of course, divisibility by 2 and 3 is just checking if the last digit is divisible by two or three. Do this by looking at the last digit of the last digit.
Numbers up to 145 get to keep their normal Misalian names, but after that, 1:000 is called "seleven". So a number like 145:002 is pronounced "nif foursy five seleven and two".
Then 1:0:0 is called "nifail", becuase it's equal to nif times a failure. This is a reference to disgustimal. After that is 1:0:0:0, which is called "seleven nifail". A number like 35:112:130:53 is pronounced "thirsy five seleven and nif eight nifail, nif thirsy seleven and fifsy three".
1:0:0:0:0 is called "unexedy", as it's equal to unexian times a tragedy. Again a reference to disgustimal. Numbers bigger than 145:145:145:145:145:145:145:145 are currently unnamed. 15012 - 1 is a big number though. Oh, and if the naming scheme wasn't clear:
| 1 | One |
| 1:0 | Seleven |
| 1:0:0 | Nifail |
| 1:0:0:0 | Seleven nifail |
| 1:0:0:0:0 | Unexedy |
| 1:0:0:0:0:0 | Seleven unexedy |
| 1:0:0:0:0:0:0 | Nifail unexedy |
| 1:0:0:0:0:0:0:0 | Seleven nifail unexedy |
| 1:0:0:0:0:0:0:0:0 | Technically unnamed, you can call it "sixunexicide" if you want tho |
Okay thank you for reading my silly lil webpage, sorry that it was shorter than normal.