# Primes

represents the domain of prime numbers, as in xPrimes.

# Details • xPrimes evaluates only if x is a numeric quantity.
• Simplify[exprPrimes] 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 .

# Examples

open allclose all

## Basic Examples(3)

The number is a prime:

Fermat's little theorem:

Find primes satisfying an inequality:

## Scope(4)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain for Reduce and FindInstance:

## Applications(2)

A list of twin primes:

Check:

## 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: