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

Initial values

The initial values of Euclid numbers for $k=0,1,2,3,4,\dots$ are given as:

2, 3, 7, 31, 211, 2311, View list on OEIS