If you change the prime number 13 to base 7 you get 16. How can 16 be a prime number? Is it that 16 base 7 is a prime number in base 7 math? Can you give an example of how this could be true?
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Basically, changing a number’s base doesn’t change anything about a number’s properties. The only thing that changes is how we write it.
>How can 16 be a prime number?
Because 16 is not even in base 7. The reason that we only have to check the last digit in base 10 to determine whether a number is even or not is because 10 itself is also even and therefore adding any number of 10s or its powers will not affect a number’s evenness – this is not the case in base 7.
10 looks even to us because we’re used to base 10, but if it is in base 7 and we subtract 2 from it – we get 5, which is odd, and looks odd to us in both base 7 and base 10.
Note that I’ve largely talked about evenness rather than primeness, and this is because I assume that your question about 16 in base 7 comes from it “looking” even (and therefore not prime) because we’re used to base 10.
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