# Euler Lucky Number/Examples/3

## Example of Euler Lucky Number

The expression:

$n^2 + n + 3$

yields primes for $n = 0$ to $n = 1$.

This demonstrates that $3$ is (more or less trivially) a Euler lucky number.

## Proof

 $\displaystyle 0^2 + 0 + 3$ $=$ $\displaystyle 0 + 0 + 3$ $\displaystyle = 3$ which is prime $\displaystyle 1^2 + 1 + 3$ $=$ $\displaystyle 1 + 1 + 3$ $\displaystyle = 5$ which is prime

$\blacksquare$