1,1

Note that (n^n-1)/(n-1) is prime only if n is prime, in which case it equals cyclotomic(n,n), the n-th cyclotomic polynomial evaluated at x=n. This sequence is a subset of A070519. The number cyclotomic(7547,7547) is a probable prime found by H. Lifchitz. Are there only a finite number of these primes?

Contribution from T. D. Noe (noe(AT)sspectra.com), Dec 16 2008: (Start)

The standard heuristic implies that there are an infinite number of these primes and that the next n should be between 10^10 and 10^11.

Let N = (7547^7547-1)/(7547-1) = A023037(7547). If N is prime, then the period of the Bell numbers modulo 7547 is N. See A054767. (End)

R. K. Guy, Unsolved Problems in Theory of Numbers, 1994, A3.

Eric Weisstein's World of Mathematics, Cyclotomic Polynomial

Do[p=Prime[n]; If[PrimeQ[(p^p-1)/(p-1)], Print[p]], {n, 100}]

Cf. A070519 (cyclotomic(n, n) is prime).

Cf. A056826 ((n^n+1)/(n+1) is prime).

Adjacent sequences: A088787 A088788 A088789 this_sequence A088791 A088792 A088793

Sequence in context: A058912 A040145 A142955 this_sequence A135958 A163665 A051079

hard,more,nonn

T. D. Noe (noe(AT)sspectra.com), Oct 16 2003