Are base 10 prime numbers still primes when converted to their equivalent value in another base number system?

For example, from base 10 to base 2 or base 12? What's the significance of primacy?|||Yes; the definition of primality is independent of the way we represent the numbers.|||Yes, primes are still primes. Their factors don't change.|||The numbers may look different, but they are still only divisible by themselves and one if they're prime.|||Being a prime has to do with the number of divisors a number has. How you write the number has no effect on this.





For instance, you might see this:


13(base 10) = 15(base 8)


and think that 13 is prime and 15 is composite, but you're not thinking of 15(base 8) when you think of fifteen. In fact, the English language would read 15(base 8) as thirteen.|||Yes, base 10 prime numbers are still primes when converted to other bases because they still have all the same factors they are just represented differently. One use of Prime numbers in is Cryptology.|||For example 6 is a composite number in base 10, because 6=2*3 and in binary 6=110=10*11 and 10 and 11 are 2 and 3 in binary.


But 7 is 111 and is prime and is not divisible by 10 or 11 (2 or 3) which are the only possible prime factors.


Composites remain composites with the same prime factors than in base 10 and primes remain primes.A not too difficult proof is possible.