%I A088790
%S A088790 2,3,19,31,7547
%N A088790 Numbers n such that (n^n-1)/(n-1) is prime.
%C A088790 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?
%C A088790 Contribution from T. D. Noe (noe(AT)sspectra.com), Dec 16 2008: (Start)
%C A088790 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.
%C A088790 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)
%D A088790 R. K. Guy, Unsolved Problems in Theory of Numbers, 1994, A3.
%H A088790 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CyclotomicPolynomial.html">Cyclotomic Polynomial</a>
%t A088790 Do[p=Prime[n]; If[PrimeQ[(p^p-1)/(p-1)], Print[p]], {n, 100}]
%Y A088790 Cf. A070519 (cyclotomic(n, n) is prime).
%Y A088790 Cf. A056826 ((n^n+1)/(n+1) is prime).
%Y A088790 Sequence in context: A058912 A040145 A142955 this_sequence A135958 A163665 
               A051079
%Y A088790 Adjacent sequences: A088787 A088788 A088789 this_sequence A088791 A088792 
               A088793
%K A088790 hard,more,nonn
%O A088790 1,1
%A A088790 T. D. Noe (noe(AT)sspectra.com), Oct 16 2003