Fibonacci Number with Prime Index is not necessarily Prime
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Theorem
Let $p \in \Z_{>0}$ be a prime number.
Let $F_p$ be the $p$th Fibonacci number.
Then $F_p$ is not itself necessarily prime.
Proof
- $F_{19} = 4181 = 37 \times 113$
$\blacksquare$
Also see
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $5$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $5$