“First it sounded totally unbelievable, since 37 is a tiny number in the grand scheme of things.”
Pick any integer at random and its second-smallest prime factor is below 37 about half the time. The claim sits in the preface of Those Fascinating Numbers, and Grossack checked it in Sage instead of taking it on faith. The model predicts a density of about 0.5002501, close to what the numbers show. Huge integers are built mostly from tiny primes.