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. I'm thinking of the movie "Contact" -like evidence, where they received a message of all the prime numbers from 1-100, in order. No chance that was random noise.

But there is a chance that it is random noise. At least, not 'random' noise, but naturally generated noise.

Seemingly complex number patterns occur in nature. For instance, it's well known that sunflowers have Fibonacci sequences in their spiraling seeds.

No natural phenomenon is known that generates prime numbers, but if there were such a thing, I bet it would work on the principle of the Sieve of Erathosthenes.
It could be generating all numbers, but multiples of previous numbers are filtered out somehow.
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