Why prime numbers? Or as some have suggested, the Fibonacci series.
I know they have played a great role in the historical development of mathematics, but as far as I can tell they have no engineering applications. And I don't recall them playing any role in calculus, differential equations, linear algebra or numerical analysis.
Its conceivable a civilization could have great engineering achievements and simply not give a fig about number theory.
No, I would just transmit the the first few real numbers, 1, 2, 3, ... and so on. I can't think of that arising in any natural process. that is, they would be immediately identified as an artifact, not some physical manifestation.