We haven't been able to decode what whales and dolphins are communicating. Are they using language? A problem SETI faces is whether we would be able to decode an alien signal. They may be too different in their biology, culture and technology. The book & movie Contact propose that math is a universal language. This assumes they're motivated to use the same basic mathematical structures we do. Maybe they don't care about prime numbers.

Solaris by Stanislaw Lem explores an alien ocean that so different humans utterly fail to communicate with it, leading to the ocean creating humans from memories in brain scans broadcast over the ocean, but it's never understood why the ocean did this. The recreated humans don't know either.