Talk:Prime to Own Power minus 1 over Prime minus 1 being Prime

In Unsolved, page 10, section A3, Guy writes:
 * Wagstaff observes that the only primes $<180$ for which $(p^p-1)/(p-1)$ is prime are $p = 2, 3, 7, 19, 31$; for $(p^p+1)/(p+1)$ they are $3, 5, 17, 157$.

However, note that:
 * $\dfrac {7^7 - 1} {7 - 1} = 137257 = 29 \times 4733$, suggesting this error was inherited from Guy & Wagstaff
 * A088790 states that $\dfrac {7547^{7547} - 1} {7547 - 1}$ is a probable prime.

In fact there is an elementary proof of $4 p + 1 \divides \dfrac {p^p - 1} {p - 1}$ for $p, 4 p + 1$ prime in Wagstaff's article THE PERIOD OF THE BELL NUMBERS MODULO A PRIME.

We have $7 \times 4 + 1 = 29$. --RandomUndergrad (talk) 13:36, 15 August 2020 (UTC)


 * Oops. This will need to be sorted out. --prime mover (talk) 13:49, 15 August 2020 (UTC)


 * Guy has corrected this in UPiNT 3ed. --prime mover (talk) 13:53, 15 August 2020 (UTC)


 * That's everything documented that I have been able to find. --prime mover (talk) 14:35, 15 August 2020 (UTC)