Difference between revisions of "Factorial prime"

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(Occurrence)
(Occurrence)
 
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===Initial values===
 
===Initial values===
  
The initial values of factorial primes are given as: <section begin="list"/>[[2]], [[3]], [[5]], [[7]], [[23]], [[719]], [[Oeis:A088054|View list on OEIS]]<section end="list"/>
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The initial values of factorial primes are given as: <section begin="list"/>[[2]], [[3]], [[5]], [[7]], [[23]], [[719]], [[5039]], <toggledisplay>39916801, 479001599, 87178291199, 10888869450418352160768000001, 265252859812191058636308479999999, 263130836933693530167218012159999999, 8683317618811886495518194401279999999</toggledisplay> [[Oeis:A088054|View list on OEIS]]<section end="list"/>
  
 
The first four primes <math>2,3,5,7</math> are factorial primes. However, factorial primes become much rarer after that. The next two factorial primes are <math>23</math> and <math>719</math>.
 
The first four primes <math>2,3,5,7</math> are factorial primes. However, factorial primes become much rarer after that. The next two factorial primes are <math>23</math> and <math>719</math>.

Latest revision as of 17:38, 3 July 2012

This article defines a property that can be evaluated for a prime number. In other words, every prime number either satisfies this property or does not satisfy this property.
View other properties of prime numbers | View other properties of natural numbers

Definition

A factorial prime is a prime that differs from a factorial by . In other words, it is a prime of the form .

Occurrence

Initial values

The initial values of factorial primes are given as: 2, 3, 5, 7, 23, 719, 5039, [SHOW MORE] View list on OEIS

The first four primes are factorial primes. However, factorial primes become much rarer after that. The next two factorial primes are and .

The initial values of for which is prime are . Note that, by Wilson's theorem, cannot be prime if is prime, for . This explains, for instance, why and are not prime. are also Brown numbers -- they are solutions to Brocard's problem of being a perfect square.

The initial values of for which is prime are: .