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 A088790 Numbers n such that (n^n-1)/(n-1) is prime. 8
 2, 3, 19, 31, 7547 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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, 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) REFERENCES R. K. Guy, Unsolved Problems in Theory of Numbers, 1994, A3. LINKS Bernard Schott, Les nombres brĂ©siliens, Quadrature, no. 76, avril-juin 2010, pages 30-38; included here with permission from the editors of Quadrature. Eric Weisstein's World of Mathematics, Cyclotomic Polynomial MATHEMATICA Do[p=Prime[n]; If[PrimeQ[(p^p-1)/(p-1)], Print[p]], {n, 100}] PROG (PARI) is(n)=ispseudoprime((n^n-1)/(n-1)) \\ Charles R Greathouse IV, Feb 17 2017 CROSSREFS Cf. A070519 (cyclotomic(n, n) is prime). Cf. A056826 ((n^n+1)/(n+1) is prime). Sequence in context: A040145 A142955 A213896 * A283186 A215304 A215281 Adjacent sequences:  A088787 A088788 A088789 * A088791 A088792 A088793 KEYWORD hard,more,nonn AUTHOR T. D. Noe, Oct 16 2003 STATUS approved

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Last modified January 24 04:21 EST 2021. Contains 340398 sequences. (Running on oeis4.)