Cool, but these numbers don't have to be primes. They just have to be coprimes (like (8,9)).
The least common multiple of two coprimes 'a' and 'b' is a*b.
The least common multiple of two coprimes 'a' and 'b' is a*b.
In the cicada example the point is that one predator would evolve to align its boom cycle so that it had a common divisor with the cycle of the cicada.
Since the predator's cycle is variable, it is evolutionarily optimal if the cicada only comes out every prime number of years.
It's important to note that, for the cicada, they are not a staple diet but rather an opportunistic one that occurs only once in a few generations. This means that the predator's cycle would have to skip generations in order to be effective. This is unlikely, given that that cycle would have no evolutionary advantage in the intermediary, and would thus be diluted by more pressing concerns.
The other relevant barrier we have is probably that a 6-year wasp has difficulty stretching its cycle by a factor of 3--much more difficult than a single year or two.