Euclid number: Difference between revisions
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==Definition== | ==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 <math>k</math> primes for some nonnegative integer <math>k</math>. In symbols it is <math>k\# + 1</math>. | A '''Euclid number''' is a number that is one more than a [[defining ingredient::primorial]]. In other words, it is one more than the product of the first <math>k</math> primes for some nonnegative integer <math>k</math>. In symbols it is <math>k\# + 1</math>. | ||
A Euclid number that is prime is termed a [[Euclid prime]]. A closely related notion is that of [[factorial prime]]. | A Euclid number that is prime is termed a [[Euclid prime]]. A closely related notion is that of [[factorial prime]]. | ||
==Behavior== | ==Behavior== | ||
===Initial values=== | ===Initial values=== | ||
The initial values of Euclid numbers for <math>k=0,1,2,3,4</math> are < | The initial values of Euclid numbers for <math>k=0,1,2,3,4,\dots</math> are given as: <section begin="list"/>[[2]], [[3]], [[7]], [[31]], [[211]], [[2311]], [[Oeis:A006862|View list on OEIS]]<section end="list"/> | ||
Latest revision as of 01:10, 23 June 2012
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:
