>Finding a message would be hugely significant, even if we're too dumb to decode it.

That is actually what the majority of my above mentioned His Master's Voice is about - is this relatively regularly appearing signal a message? Or is it just regularly looking noise from some physical object we haven't discovered yet?

If that regular noise produces prime numbers, it is very unlikely to be natural. Species that have the ability to send signals into space also have the ability to show their intelligence. Whether actual communication is possible is a different question.

All the white noise of the sun could indeed just be part of the galactic network, of which we have not yet discovered the keys .. so it may look like white-noise until we find the key. I'm happier with that position than that, so far, we just don't know the message because there has not been a 'good one we can understand easily', i.e. ufo on the whitehouse lawn ..

Old Egyptian developed and was never meant to be "decrypted" from scratch.

Some thing will have to be the same for the aliens. Some things like mathematics (Pi, Pythagoras, Primes). If you send a message that needs to be understood, send mathematical information.