# Euclid number

From 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 primes for some nonnegative integer . In symbols it is .

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 are given as: 2, 3, 7, 31, 211, 2311, View list on OEIS