42 is special, though, as the longest cycle that requires a its own solution. 43+ can be made as a Snark Loop.

https://conwaylife.com/wiki/P43_Snark_loop

That doesn't make any sense to me. A 6-cycle oscillator next to a 7-cycle oscillator should form a 42-cycle oscillator, or am I missing something?

This paper is primarily considering nontrivial oscillators, i.e., oscillators in which at least one cell oscillates at the full period, not just some divisor. Still, there are many nontrivial "LCM" oscillators that can be constructed with two lower-period oscillators that just slightly interact. Such an LCM oscillator for p42 ("unix on 44P7.2") could have been constructed for decades; the actual last nontrivial periods to be discovered were p34, p38, p19, and p41.

Off by one

Or if 42 was the only impossible period.

If you care for 42 to be special, here's video that might be of interest to you.

The Answer to the Ultimate Question of Life, the Universe and Everything :

https://www.youtube.com/watch?v=ZFxT0sObrYQ