Euler Lucky Number/Examples/3

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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

$\blacksquare$