--- In

primenumbers@yahoogroups.com, "julienbenney" <jpbenney@f...>

wrote:

> Moving away from prime quadruples, there is another topic that I

have

> never seen anything written about that I am curious about.

>

> I know from tables of generalised repunit primes that

((n^n)-1)/(n-1)

> is prime for n = 2, 3, 19 and 31 and for no other n up to 1,000. Is

> there a theorem that could show these four numbers to be the only n

for

> which ((n^n)-1)/(n-1) is prime?

>

> Also, when was the primality of 19^19-1/18 and 31^31-1/30 proved?

[I am

> curious]

The next value of n that yields a probable prime is 7547. See

sequence A088790 has more information.

Tony