Thinking further, primes become less frequent because they are defined that way - once a number is identified as prime, it wipes out all multiples of it. Like

Thinking further, primes become less frequent because they are defined that way - once a number is identified as prime, it wipes out all multiples of it. Like the integers, the number of possible combinations of things is infinite. The issue is what proportion of them are "improvements". Perhaps an approach is to try to define what makes something an "improvement": if you brute search many combinations, how do you determine whether a combination is an "improvement" (and in which way)? Is it independent of how many we've looked at before (like primes)?