Euclid number

This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers

Definition

A Euclid number is a number that is one more than a primorial. In other words, it is one more than the product of the first $k$ primes for some nonnegative integer $k$. In symbols it is $k\#+1$.

A Euclid number that is prime is termed a Euclid prime. A closely related notion is that of factorial prime.

Behavior

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A006862

Initial values

The initial values of Euclid numbers for $k=0,1,2,3,4$ are $2,3,7,31,211$.