A prime is an integer greater than 1 divisible only by 1 and itself. Every integer greater than 1 is either prime or a unique product of primes: the Fundamental Theorem of Arithmetic.
Euclid proved around 300 BC that there are infinitely many primes. The Prime Number Theorem describes their distribution: primes up to N ≈ N/ln(N). The Riemann Hypothesis: the deepest unsolved problem in mathematics: predicts the precise distribution of prime gaps.
MemorisePi lets you memorise the first 1000 primes using the same numpad muscle-memory technique as pi.