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Home > Factorial prime

A factorial prime is a number that is one less or one more than a factorial and is also a prime number. The first few factorial primes are: 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199, ...

Factorial primes are of interest to number theorists because they sometimes signal the end or the beginning of an extraordinarily lengthy run of consecutive composite numbers. For example, the prime following 479,001,599 is 479,001,629.

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Number theory

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Topics: Factorial Prime, Factorial Moment...

FactorialNumber theory Combinatorics In mathematics, the factorial of a natural number n is the product of the positive integers less than or equal to n''. This is written as n and pronounced n factorial". The notation n was introduced by Christian Kramp in 1808.Factorial primeA factorial prime is a number that is one less or one more than a factorial and is also a prime number. The first few factorial primes are: 2, 3, 5, 7, 23, 719, 5039, 39916801, 479001599, 87178291199,. Factorial primes are of interest to number theoristsFactorial momentIn probability theory, the n''th factorial moment of a probability distribution, also called the n''th factorial moment of any random variable X with that probability distribution, is : where : is the falling factorial (confusingly, this same notation, th
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