Sieve of Eratosthenes — eliminating composites to reveal primes
Eratosthenes (c. 240 BCE): mark multiples of each prime as composite. Remaining unmarked numbers are prime.
Prime Number Theorem: π(N) ~ N/ln(N). The ratio approaches 1 as N→∞. Twin prime conjecture (unsolved): infinitely many pairs {p, p+2}.