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 . This typeset form can be input using pris.
Examplesopen allclose all
Basic Examples (3)
Test domain membership of a numeric expression:
Make domain membership assumptions:
Specify the default domain for Reduce and FindInstance:
Wilson's theorem [more info]:
Properties & Relations (3)
Primes is contained in Complexes, Reals, Algebraics, Rationals, and Integers:
Simplifications involving prime numbers:
Primes represents the set of positive integers that are prime:
PrimeQ gives True if an integer, positive or negative, is prime:
PrimeQ returns True for explicit numeric primes and False otherwise:
Element remains unevaluated when it cannot decide whether an expression is a prime:
Wolfram Research (1999), Primes, Wolfram Language function, https://reference.wolfram.com/language/ref/Primes.html (updated 2017).
Wolfram Language. 1999. "Primes." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Primes.html.
Wolfram Language. (1999). Primes. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Primes.html