Binary I could see because on and off is universal ... ascii is to "earthbound" ... it's only been around since computers ... unless you drift into thinking our use of that came from alien tech ....?
Even general math is questionable... Is a primary number in base 10, still a primary if converted to hex .. or base 7 ...?
Geometry is universal, too...
Google and you shall receive:
A prime is a prime no matter which base you use to represent it. On http://mathforum.org/library/drmath/view/55880.html
the surface one might think that in Hex you would have 3*5 = 15 as
"usual," but it really turns out that 3*5 = F.
The example 21 doesn't work too well because it is not prime.
The base ten number 37 is better, because it is prime, but its Hex
representation is 25, which sort of looks non-prime. Hex 25 is not,
however, repeat not, 5 squared.
Okay, enough for examples. The fact of being prime or composite is
just a property of the number itself, regardless of the way you write
it. 15 and F and Roman numeral XV all mean the number, which is 3
times 5, so it is composite. That is the way it is for all numbers, in
the sense that if a base ten number N has factors, you can represent
those factors in Hex and their product will be the number N in Hex.
Relating to your question about base 13, the base ten number 13 will
be represented as "10" in that system, but "10" will still be a prime,
because you cannot find two numbers other than 1 and "10" that will
multiply together to make "10".
I hope this helps you think about primes in other bases.