Either way though, prime number distribution is quite tricky - we should probably be looking in other number bases as well rather than just base 10. This inter

Either way though, prime number distribution is quite tricky - we should probably be looking in other number bases as well rather than just base 10. This interested me so I went looking for how primes would work in other bases, this answer implies that primes are the same regardless of base: A prime is a prime no matter which base you use to represent it. On the surface one might think that in Hex you would have 35 = 15 as "usual," but it really turns out that 35 = 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. [1] http://mathforum.org/library/drmath/view/55880.html http://mathforum.org/library/drmath/view/55880.html