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So, yes, if we send a Wolfram|Alpha, we’re sending knowledge of our civilization in a concentrated, computational form, ready to be used as broadly as possible. Of course, at least the public version of Wolfram|Alpha is just about general, public knowledge. So what about more ...
Nowadays, with Mathematica and the Wolfram Language, it’s easy to test things like this: Back in 1954, Sol had to do all this by hand, but came up with a fairly long table of primitive polynomials corresponding to shift registers that give maximal length sequences: The Prehistory of ...