[OscarCunningham]

I also used to think that there weren't very many primes. But the prime number theorem says that the number of primes less than n is about n/log(n). The function log doesn't grow very fast, so a large proportion of numbers are prime. For example the number of primes less than 10^100 is 4*10^97.

Primes are really really common.

[soVeryTired]

Much more common than square numbers, for example. sum(1/n^2) converges, but sum(1/p) for p prime doesn't.