# Definition:Fermat Pseudoprime/Base 4/Mistake

## Source Work

The Dictionary
$217$

## Mistake

The second smallest pseudoprime to base $4$ ($15$ is the smallest).
$4^{216} - 1$ is divisible by $217$ although $217$ is not prime but $7 \times 31$.

## Correction

The author is correct in that $217$ is indeed not prime, but $7 \times 31$.

Also, $15$ is the smallest pseudoprime to base $4$.

However, $217$ is not a pseudoprime to base $4$.

It is in fact the $3$rd pseudoprime to base $5$:

$5^{216} - 1$ is divisible by $217$.

In David Wells: Curious and Interesting Numbers (2nd ed.), this section has been removed.