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): $217$