A prime number has exactly two factors: 1 and itself. The first primes are 2, 3, 5, 7, 11, 13. The number 2 is the only even prime. The number 1 is not prime because it has only one factor.

Primes are the building blocks of the integers. Every integer greater than 1 factors uniquely into primes, a result called the fundamental theorem of arithmetic. Euclid proved there are infinitely many primes. Their distribution remains a deep mystery, connected to the Riemann hypothesis.

Primes are essential in cryptography. RSA encryption relies on the difficulty of factoring large numbers into primes. Primality testing and prime generation are active areas of computational number theory. Despite their simple definition, primes hold some of mathematics' deepest secrets.

• Natural number greater than 1 with exactly two factors
• 2 is the only even prime
• Infinitely many primes (Euclid)
• Central to RSA encryption