[abetusk]

From the abstract:

""" ... At the turn of the millennium, only twelve oscillator periods remained ... . The search has finally ended, with ... the final two periods, 19 and 41, ... """

Note that 19 and 41 are prime.

I'm not familiar with this line of research in the GoL (nor most others) but I assume that it was proved all prime periods (above 41, say) have been known since the turn of the century, or thereabouts.

I suspect what happened is that there were "easy" constructions for large periods that could be done. I would think that once you have the freedom of large periods, you can construct large gadgets and thus prove with "relative ease" that you can get any large prime number period.

My bet is that smaller periods are harder because of the smallness restriction.