A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The first prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... The number 2 is the only even prime. Every integer greater than 1 can be uniquely expressed as a product of primes (Fundamental Theorem of Arithmetic). Prime numbers are crucial for cryptography (RSA encryption), where the difficulty of factoring large primes ensures security.
Prime numbers were studied by the ancient Greeks. Euclid proved there are infinitely many primes (300 BCE). The Sieve of Eratosthenes provides a method to find primes. The Riemann Hypothesis (1859), one of mathematics' greatest unsolved problems, concerns the distribution of primes.