Primes

Primes

represents the domain of prime numbers, as in x∈Primes.

Details

  • 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 TemplateBox[{}, Primes]. This typeset form can be input using pris.

Examples

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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:

TraditionalForm formatting:

Applications  (2)

Wilson's theorem [more info]:

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:

Wolfram Research (1999), Primes, Wolfram Language function, https://reference.wolfram.com/language/ref/Primes.html (updated 2017).

Text

Wolfram Research (1999), Primes, Wolfram Language function, https://reference.wolfram.com/language/ref/Primes.html (updated 2017).

CMS

Wolfram Language. 1999. "Primes." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Primes.html.

APA

Wolfram Language. (1999). Primes. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Primes.html

BibTeX

@misc{reference.wolfram_2024_primes, author="Wolfram Research", title="{Primes}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Primes.html}", note=[Accessed: 22-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_primes, organization={Wolfram Research}, title={Primes}, year={2017}, url={https://reference.wolfram.com/language/ref/Primes.html}, note=[Accessed: 22-December-2024 ]}