PrimeQ[expr] yields True if expr is a prime number, and yields False otherwise.
PrimeQ gives False.
PrimeQ[-n], where n is prime, gives True.
PrimeQ[n, GaussianIntegers->True] determines whether n is a Gaussian prime.
Simplify[expr Primes] can be used to try to determine whether a symbolic expression is mathematically a prime.
See The Mathematica Book: Section 2.3.5, Section 3.1.1 and Section 3.2.4.
Implementation Notes: see section A.9.4.
See also: FactorInteger, Primes.
Related package: NumberTheory`PrimeQ`.