We know that DNA contains information because it produces humans, dogs, cats, kangaroos, black ones, white ones.... And those beget other humans, dogs, cats.... Were it random, you would be no more likely to have a human baby than a puppy. For that matter, a random DNA sequence would never produce such a complex, well-oiled machine as an organism in the first place.
Informational signatures cannot be EASILY detected, or with 100% certainty. Your example contains much more information than just prime numbers, though: you have a serial bitstream of 1's and 0's. These are RF transmissions we're talking about. The mere detection of a digitized bitstream within a statistically-impossible spectral concentration would singlehandedly indicate intelligent life. And by that I don't just mean an analog signal you can take the 90/10 point of (obviously all analog has that quality). I mean repeated digital patterns which do not repeat if you analyze the same signal as an analog waveform.
Or--the far more likely outcome--that someone can match the RF signature with a known astrophysical phenomenon. At that point it becomes neither random nor information, nor intelligent life: that is ordered spontaneity. We have an international community of very bright people in multiple fields; not to mention Big Data. We have a good chance to figure it out.
