Primes Hide the Deepest Puzzle

Primes look simple — but they hide the Riemann Hypothesis, considered the single most important unsolved problem in mathematics. A $1 million prize from the Clay Institute awaits a proof. The conjecture describes a pattern in how primes thin out among the integers.

Even without proof, the Prime Number Theorem (1896) says the nth prime is near n × ln(n) — primes become rarer as numbers grow. And yet twin primes — pairs like (11, 13) or (17, 19) — appear to go on forever, though this has not been proven. The gap between what we know about primes and what we can prove is one of the oldest and widest in math.