I recommend having instant recognition of all the powers up to 2^24, this has proven very useful over the years e.g. when skimming quickly through a log searching for anomalies, flag patterns etc. If you recite them in sequence twice a day for a couple of weeks, then they’ll stick in your mind for decades. I can say from experience this method also works for the NATO phonetic alphabet, Hamlet’s soliloquies, ASCII, and mum’s lemon drizzle cake recipe. It fails however for the periodic table, ruined forever by Tom Lehrer.

Ever the quandary: satisfy some people completely, or a larger number but incompletely.

I concur with the suggestion of 2^19, because even though fewer people would recognize it immediately, many of them would question the significance, and their eventual realization would be more satisfying.