IDK why, but this factoid blowing my mind right now.
One of the ways to broadcast evidence of Math + Computing power could be to calculate this constant to an absurd-enough precision and have SETI (or someone) send the digits out into space.
Edit: in the sense that, we know how to encode a large set of primes in a single transcendental number, and by the way, here it is.
I'm not sure why you ask? The above number already showed off the transition between 1 and 2 digit primes. And 0s inside the primes should not be a problem.
Hmmm, what's the algorithm to extract 101 and not 10101 or 1010103 as the next prime? I suppose you can remember how many digits were in the last prime and only allow the same or 1 more, which should be unambiguous. Though it relies on the unproven conjecture that there are no very long runs (an entire order of magnitude!) with no primes.
The point is, with a constructed transcendent number, you can represent any series at all, so long as you have "enough precision."
That last part means you can simply adjust your precision to your desired constraints. If you want to unambiguously represent the primes up through all the four-digit primes, simply change your padding accordingly: 0.000200030005....
Obviously the Buenos Aires Constant in the article is a neater representation, and relies on neater math. But GP's point was that you can stuff anything at all into a transcendent number.
Even if that ambiguity did exist, it would just complicate the issue of extracting primes from the sequence. It wouldn't complicate recognizing the sequence.
One of the ways to broadcast evidence of Math + Computing power could be to calculate this constant to an absurd-enough precision and have SETI (or someone) send the digits out into space.
Edit: in the sense that, we know how to encode a large set of primes in a single transcendental number, and by the way, here it is.