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Mathematica > Mathematics and Algorithms > Formula Manipulation > Assumptions and Domains > Primes >

BUILT-IN MATHEMATICA SYMBOL

Primes

Primes
represents the domain of prime numbers, as in x

Primes.

Simplify can be used to try to determine whether an expression corresponds to a prime number.

The number

is a prime:

Fermat's little theorem:

Find primes satisfying an inequality:

The number

is a prime:

Out[1]=

Fermat's little theorem:

Out[1]=

Find primes satisfying an inequality:

Out[1]=

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain for Reduce and FindInstance:

Wilson's theorem :

A list of twin primes:

Check:

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: