Factorial prime
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.
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Definition
A factorial prime is a prime that differs from a factorial by . In other words, it is a prime of the form .
Occurrence
The ID of the sequence in the Online Encyclopedia of Integer Sequences is A088054
Initial values
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: .