Somehow last night I stumbled on The Prime Pages, published by The University of Tennessee Martin. One of the pages has a list of Mersenne Primes and the year of their discovery. This is interesting because to some extent the number of known primes reflects technological progress and also economic growth since devoting resources to finding primes has an opportunity cost. It’s also not often that we get a robust 500-year time series to look at.
Here is a chart of the cumulative number of known Mersenne primes over time:
There is a slight flattening of the curve at the last point: have we reached diminishing returns? It’s probably too early to tell.