# Definition:Euclid Prime

## Definition

A Euclid prime is a natural number which is both a Euclid number and a prime number.

### Sequence of Euclid Primes

The sequence of Euclid primes begins:

$2, 3, 7, 31, 211, 2311, 200 \, 560 \, 490 \, 131, \ldots$

### Sequence of Non-Prime Euclid Numbers

The sequence of Euclid numbers which are not prime begins:

$30 \, 031, 510 \, 511, 9 \, 699 \, 691, 223 \, 092 \, 871, 6 \, 469 \, 693 \, 231, 7 \, 420 \, 738 \, 134 \, 811, \ldots$

## Source of Name

This entry was named for Euclid.