Vipul: Created page with '{{prime number property}} ==Definition== A ''Euclid prime''' is a prime number that is one more than a defining ingredient::primorial. In other words, it is a prime num...'

2009-04-30T21:17:40Z

Created page with '{{prime number property}} ==Definition== A ''Euclid prime''' is a prime number that is one more than a defining ingredient::primorial. In other words, it is a prime num...'

New page

{{prime number property}}

==Definition==

A ''Euclid prime''' is a [[prime number]] that is one more than a [[defining ingredient::primorial]]. In other words, it is a prime number of the form <math>k\# + 1</math>, where <math>k\#</math> denotes the product of the first <math>k</math> primes.

A natural number of the form <math>k\#+ 1</math> is termed a [[defining ingredient::Euclid number]], so a Euclid prime is a Euclid number that happens to be prime.

==Occurrence==

{{oeis|A018239}}

===Initial values===

The initial values of Euclid numbers are prime. For <math>k=0,1,2,3,4,5</math>, the corresponding Euclid numbers <math>2,3,7,31,211,2311</math> are prime. The first Euclid number that is not prime is <math>30031</math>, corresponding to <math>k = 6</math>.

Euclid prime - Revision history

Vipul: Created page with '{{prime number property}} ==Definition== A ''Euclid prime''' is a prime number that is one more than a defining ingredient::primorial. In other words, it is a prime num...'