Base"Lang"

Classification
This isn't a lang, it's more like a standart for refering to bases.

It's inspired by this video: https://www.youtube.com/watch?v=7OEF3JD-jYo

Roots
0 and 1 are nullary and unary

The other bases are derived form prime bases + base prefixes

2-20 primes has names 13 is the bad luck number

19 doesn't have a base name, but spain has 19 autonomous comunities

Derivation
For +20 primes, you can put un- to create the n+1 number or negun- or - to make the n-1 number.

If a composite number is a power of a prime number, you can use -plexic as an adjective to use in the standalone base name (biplexic binary, being base 4), if you wanna include it in the name, use -plexo-, thats the prefix form of -plexic (biplexic become biplexo-, biplexobinary for biplexic binary)

If you need the prefixable version of a composite number, substitude the -y or -al for -o (binaro, trinaro, quinaro, septaro, elevenaro, demonaro, suboptimo, spanaro)

Checks
First, check if the number is an integer, if it's a negative integer, use is positive equivalent and then use the prefix nega- (negabinary, negabiquinary).

if there are 0 or 1, use their names (nullary or unary)

Main Part
Make the list of divisors of the number to encode, then divide the number by their biggest divisor without being itself, now organize it, first the cocient (the small number) then the divisor (the big number), and then answer the question: are both numbers encodable?, if not, then check if it is unencodable because of one of them being a prime, if it is, use the prefixes negun- or un- to subtact or add one to the prime, then do the same to the new composite number. if a composite number isn't encodable, do the same to the composite number (that is, jump to the beggining of this paragraph using your new number)

Composing the number
Now, with all of the numbers organized and decomposed into primes, use the roots and prefixes, of the first main part numbers you did separate, the left one will be a prefix and the right one will be a base name, if there aren't encodable, you do that recursively (24 > 2-12 > 2-(2-6) > 2-(2-(2-3))) until all of them are encodable. if any of the prefixes is a composite number use their prefixable forms, if you have two suffixes before a base number, normally the prefixes are fused (2-(2-(2-3)) > (2-2)-(2-3) > biplexobinarobitrinary)