# Euclid 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 Euclid prime' is a prime number that is one more than a primorial. In other words, it is a prime number of the form , where  denotes the product of the first  primes.

A natural number of the form  is termed a Euclid number, so a Euclid prime is a Euclid number that happens to be prime.

## Occurrence

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A018239

### Initial values

The initial values of Euclid numbers are prime. For , the corresponding Euclid numbers  are prime. The first Euclid number that is not prime is , corresponding to .