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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Base 10 is just a way we represent numbers. The numbers themselves are just that… numbers. 92 in base 10 is 10 in base 92, but physically it is still 92 objects. Prime numbers are dependent on the absolute numbers, not their representation, and hence are the same irrespective of the base you use.
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