Euclid prime

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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.
View other properties of prime numbers | View other properties of natural numbers


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.


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 .