Prime numbers are positive integers that are divisible only by themselves and 1. The first eleven are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, and 31, but there are infinitely many. By convention, 1 is not considered prime, while 2 is the only even prime. A number that is neither 1 nor a prime is called a composite number.
Every composite number can be written uniquely as a product of prime factors multiplied together: for example, 12 = 22 × 3, 21 = 3 × 7, and 270 = 2 × 33 × 5. Since prime numbers cannot be factorized themselves, they can be thought of as the fundamental building blocks of positive integers. However, determining whether a number is prime, and finding the prime factors if it is not, can be extremely difficult. This process is therefore an ideal basis for encryption systems.
There are many deep patterns to the primes, and one of the great outstanding hypotheses of mathematics, the Riemann hypothesis, is concerned with their distribution.
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