# Difference between revisions of "Factorial prime"

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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"/> | + | 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 OEISThe 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: .