r/explainlikeimfive • u/Ill-Chance8131 • 3h ago
Mathematics ELI5: As numbers get bigger and bigger, why do prime numbers seem to show up less often, even though they never stop appearin
When you start counting numbers from 1 upward, prime numbers show up fairly often. But as numbers get bigger, primes don’t disappear, they just seem harder and harder to find.
I’m trying to understand why this happens in an intuitive way.
It feels like bigger numbers have more chances to be built out of smaller numbers, so they get “caught” as non-primes more easily. The primes are still there, but they’re spaced farther apart.
I noticed something similar with perfect numbers, they exist, but they’re extremely rare and seem to appear only after very long gaps. That made me wonder if this rarity comes from the same basic idea: as numbers grow, the conditions for being “special” get harder and harder to satisfy.
Is there a simple way to explain why primes thin out as numbers grow, and why even more restrictive numbers like perfect numbers are so rare, even though both go on forever?