Primorial 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.
View other properties of prime numbers | View other properties of natural numbers

Definition

A primorial prime is a prime number that differs from a primorial by $1$.

In other words, it is a prime number of the form $k\#\pm 1$.

The primorial primes of the form $k\#+1$ are also called Euclid primes, and all numbers of the form $k\#+1$ are called Euclid numbers.

Behavior

Initial values

The initial values of primorial primes are $2,3,5,7,29,31,211$.