This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
 Prime Numbers The primes have been a focal point for investigations of numbers for more than two millennia. Mathematica implements state-of-the-art algorithms for handling both primes and the advanced mathematics that has grown up around their study. Use Prime to quickly find the billionth prime, or Zeta to get empirical evidence related to the Riemann hypothesis. Generating Primes Prime — the nth prime number NextPrime — next, previous, etc. prime RandomPrime — pick a random prime Sequence of Primes PrimePi — the number of primes up to n Zeta — Riemann zeta function ZetaZero — zeros of the zeta function Primality Testing PrimeQ — test if a number is prime CoprimeQ — test if numbers are coprime Theorems & Equations Primes — the domain of primes Reduce — reduce equations over the primes FindInstance — find Diophantine solutions over the primes FullSimplify — simplify assuming numbers are prime Factoring FactorInteger — find the factors of an integer TUTORIALS Integer and Number Theoretic Functions Special Functions Polynomials Modulo Primes MORE ABOUT Primality Proving Package Number Theoretic Functions Integer Functions RELATED LINKS Demonstrations related to Prime Numbers (The Wolfram Demonstrations Project)