In trying to figure out how mankind might talk with an extra-terrestrial, it seems to be a given that the extra-terrestrial would have to know about prime numbers and divisibility. Is there a simple short argument for why that should be the case? After all, humans seem to have gotten along quite a while w/o knowing anything about prime numbers, and primes only seem to have forced themselves into engineering relatively recently. There's also a potentially serious problem about the representation of numbers. We love our positional notation, but where's the proof that there aren't more interesting representations? After all, the Egyptions used (or at least some small fraction (!) of them did) used "Egyptian fractions", which is similar to partial fraction decomposition. There may be a civilization that used some sort of floating point notation (with the exponent & mantissa represented in some unspecified form) from the very start, and may never have cared at all about "integers". Of course, if ET lives in the same universe, then ET would have to know about quantum theory, so how much of quantum theory is understandable w/o any serious knowledge of primes & divisibility?