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.
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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 Failed to parse (syntax error): {\displaystyle k# \pm 1} .

The primorial primes of the form Failed to parse (syntax error): {\displaystyle k# + 1} are also called Euclid primes, and all numbers of the form Failed to parse (syntax error): {\displaystyle k# + 1} are called Euclid numbers.

Behavior

Initial values

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