Primes represents the domain of prime numbers, as in x Primes.
x Primes evaluates only if x is a numeric quantity.
Simplify[expr Primes] can be used to try to determine whether an expression corresponds to a prime number.
The domain of primes is taken to be a subset of the domain of integers.
PrimeQ[expr] returns False unless expr explicitly has head Integer.
Primes is output in TraditionalForm as .
See The Mathematica Book: Section 1.4.6 and Section 3.3.10.
See also: Element, Simplify, PrimeQ, Prime, Integers.