I’ve started reading a lot of sci-fi and the humans always attempt to communicate with aliens using prime numbers, but if they use a counting system that _isn’t_ base10, would the prime numbers still make sense?
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Bases are a way of representing numbers but they don’t affect the underlying arithmetic. It’s like how you get the same result whether you express it as two plus three equals five (English) or dos plus tres equals cinco (Spanish).
To get back to numbers, imagine you have two apples in front of you and then you add three more to wind up with five apples. You can represent that as 2+3=5 or 10+11=101 (binary) but the result has to be the same because the number of apples doesn’t depend on the “language” we describe it in.
The fact that we can do the same math in different bases is very handy because computers think in binary so they can compute in binary (or any other system) and then just translate back to base ten at the end.
Numbers are prime when they can only be divided by themselves and one. Since what divides them doesn’t depend on the base (since arithmetic doesn’t change), primes are the same in every base.
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