# Definition:Fermat Pseudoprime/Base 4/Mistake

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## Source Work

1986: David Wells: *Curious and Interesting Numbers*:

- 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.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $217$