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
| \(\ds 0^2 + 0 + 3\) | \(=\) | \(\ds 0 + 0 + 3\) | \(\ds = 3\) | which is prime | ||||||||||
| \(\ds 1^2 + 1 + 3\) | \(=\) | \(\ds 1 + 1 + 3\) | \(\ds = 5\) | which is prime |
$\blacksquare$