Prime to Own Power minus 1 over Prime minus 1 being Prime/Mistake/Wells

Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$19$

Mistake

$\paren {19^{19} - 1} / \paren {19 - 1}$ is prime. Other primes with this property are $2$, $3$, $7$ and $31$.

Untrue:

$\dfrac {7^7 - 1} {7 - 1} = 137257 = 29 \times 4733$

This mistake was inherited from 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.): $\mathbf A 3$.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $19$