Prime to Own Power minus 1 over Prime minus 1 being Prime/Mistake/Guy/Second Edition

Source Work

1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.):

$\mathbf A$: Prime Numbers

$\mathbf {A 3}$: Mersenne primes. Repunits. Fermat primes. Primes of shape $k \cdot 2^n + 1$.

Mistake

Wagstaff observes that the only primes $< 180$ for which $\paren {p^p - 1} / \paren {p - 1}$ is prime are $2$, $3$, $7$, $19$ and $31$; ...

Correction

Untrue:

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

This has been corrected in the $3$rd edition.

Sources

• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.): $\mathbf A$: Prime Numbers: $\mathbf {A 3}$: Mersenne primes. Repunits. Fermat numbers. Primes of shape $k \cdot 2^n + 1$.