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 A006794 Primes p such that -1 + product of primes up to p is prime. (Formerly M2474) 17

%I M2474

%S 3,5,11,13,41,89,317,337,991,1873,2053,2377,4093,4297,4583,6569,13033,

%T 15877

%N Primes p such that -1 + product of primes up to p is prime.

%C Or, p such that primorial(p) - 1 is prime.

%D C. K. Caldwell, On the primality of n! +- 1 and 2*3*5*...*p +- 1, Math. Comput. 64, 889-890, 1995.

%D C. K. Caldwell and Y. Gallot, On the primality of n!+-1 and 2*3*5*...*p +- 1, Math. Comp., 71 (2001), 441-448.

%D H. Dubner, Factorial and primorial primes, J. Rec. Math., 19 (No. 3, 1987), 197-203.

%D R. K. Guy, Unsolved Problems in Number Theory, Section A2.

%D R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, Arxiv preprint arXiv:1202.3670, 2012 - From _N. J. A. Sloane_, Jun 13 2012

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H C. K. Caldwell, <a href="http://primes.utm.edu/glossary/page.php?sort=PrimorialPrime">Primorial Primes</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Primorial.html">Primorial</a>

%F a(n) = A000040(A057704(n))

%t primorial[p_] := Product[Prime[k], {k, 1, PrimePi[p]}]; Select[Prime[Range[1900]], PrimeQ[primorial[#] - 1] &] (* From Jean-François Alcover, Mar 16 2011 *)

%t Transpose[With[{pr=Prime[Range[2000]]},Select[Thread[{Rest[FoldList[ Times,1,pr]], pr}], PrimeQ[ First[#]-1]&]]][[2]] (* From Harvey P. Dale, June 21 2011 *)

%Y Cf. A057704, A057705, A002110, A005234, A014545, A018239.

%K nonn,hard,more,nice

%O 1,1

%A _N. J. A. Sloane_.

%E Stated incorrectly in CRC Standard Mathematical Tables and Formulae, 30th ed., 1996, p. 101; corrected in 2nd printing.

%E Corrected by Arlin Anderson (starship1(AT)gmail.com), who reports that he and Don Robinson have checked this sequence through about 63000 digits without finding another term (Jul 04 2000).

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