It was a bit difficult to grasp at first, but it clicked after realizing it's all primes up to 37, not just 37. Kind of a neat fact, and I enjoyed reading this. Thanks for posting!
"We see that 37 is the prime where roughly half of all numbers have something less than or equal to 37 as their first prime! So we’ve proven that 37 is the median second prime!"
Can you elaborate on "it" in this sentence? What is "all primes up to 37", when you phrase things in an easier to understand way?
I can't tell if you're suggesting the word median is being used in a misleading way? But it's basically the definition of "median 37" that half your numbers are "up to 37".
I admit I read it wrong at first, but it made sense to me at the end of the article. So I don't believe median was misleading. My initial thought was, as numbers get larger and larger, the chance that the second most common prime factor is 37 so 50%, which didn't make sense because of how common 3 and 5 are. By the end I realized the function is taking into account the range of prime factors as an aggregate.
Now I understand that with enough composite numbers, the chance that their second prime factor is 37 OR BELOW converges to 50%, which is pretty neat.