Prime number

A prime number is a positive integer greater than $1$ whose only positive divisors are $1$ and itself.

Primes are the multiplicative building blocks of the positive integers. The Riemann zeta function packages information about all primes through its Euler product, and the Riemann Hypothesis is important largely because its zeros control fine features of how primes are distributed.

See also: prime factorisation, Fundamental Theorem of Arithmetic, Euler product, distribution of primes..